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Experimental Demonstration that No Tripartite-Nonlocal Causal Theory Explains Nature's Correlations
Abstract
Quantum theory predicts the existence of genuinely tripartite-entangled states, which cannot be obtained from local operations over any bipartite-entangled states and unlimited shared randomness. Some of us recently proved that this feature is a fundamental signature of quantum theory. The state |GHZ_{3}⟩=(|000⟩+|111⟩)/sqrt[2] gives rise to tripartite quantum correlations that cannot be explained by any causal theory limited to bipartite nonclassical common causes of any kind (generalizing entanglement) assisted with unlimited shared randomness. Hence, any conceivable physical theory that would reproduce quantum predictions will necessarily include genuinely tripartite resources. In this Letter, we verify that such tripartite correlations are experimentally achievable. We derive a new device-independent witness capable of falsifying causal theories wherein nonclassical resources are merely bipartite. Using a high-performance photonic |GHZ_{3}⟩ state with fidelities of 0.9741±0.002, we provide a clear experimental violation of that witness by more than 26.3 standard deviations, under the locality and fair sampling assumption. We generalize our Letter to the |GHZ_{4}⟩ state, obtaining correlations that cannot be explained by any causal theory limited to tripartite nonclassical common causes assisted with unlimited shared randomness.
... This approach resolves an anomaly [12] in earlier definitions of the GMNL concept [13][14][15] in which parallel independent twoparty nonlocality experiments can be counterintuitively classified as GMNL. The new revised notion of GMNL is named in [16] as LOSR-GMNL, with LOSR standing for local operations and shared randomness; quantum measurements of the three-way entangled GHZ state [17] can exhibit LOSR-GMNL [11,12,18] and recent experiments [19][20][21] provide some initial evidence of the phenomenon. Motivated in part by the LOSR-GMNL definition, this paper studies the general question of how to systematically model n-party conditional distributions, or behaviors, of the form P(A 1 , . . ...
... It is shown that all known three-party inequalities with two settings per party and two outcomes per setting-the simplest possible scenario witnessing LOSR-GMNL (see section SM 3 of [26])-can be derived from the inequality of Mao et al [19] (which was obtained with the inflation technique, and so the causality results of this paper reinforce the applicability of this inequality to the paradigm of wired nonsignaling resources). These derivable inequalities include the inequality of Chao and Reichardt [18] as formulated in [11] (which is notable as the Chao-Reichardt inequality had previously only been derived directly within the paradigm of wired nonsignaling resources; by deriving it here as a consequence of the inequality of Mao et al we show it holds of the more broad class of causal theories), and inequality (1) of Cao et al [20]. A second inequality of Cao et al, which has an extra setting for one of the parties, can also be derived from that of Mao et al; a natural open question is whether different inequalities can be discovered in this scenario. ...
... .,⃗ a m |x 1 , . . ., (20) and the term in brackets in (20) is equal to P i (⃗ a 1 ,⃗ a 2 , . . .,⃗ a m |x 1 , . . ...
This paper examines networks of n measuring parties sharing m nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings is causal, supporting the applicability of the inflation technique to constrain such models. For an application, we probe the example of (3,2,2) inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Mao et al (2022 Phys. Rev. Lett. 129 150401).
... Recently, genuinely tripartite nonlocal correlations have been experimentally claimed in [28][29][30]. In [28,29], employing the techniques developed in [21,31], the authors obtain novel Bell-type inequalities satisfied by tripartite correlations permissible in a strategy based on local operations on bipartite resources supplemented with globally shared local randomness, but violated by appropriate measurements on three-way entangled Greenberger-Horne-Zeilinger (GHZ) states. ...
... Recently, genuinely tripartite nonlocal correlations have been experimentally claimed in [28][29][30]. In [28,29], employing the techniques developed in [21,31], the authors obtain novel Bell-type inequalities satisfied by tripartite correlations permissible in a strategy based on local operations on bipartite resources supplemented with globally shared local randomness, but violated by appropriate measurements on three-way entangled Greenberger-Horne-Zeilinger (GHZ) states. Then these linear inequalities' violations serve as device-independent (DI) witnesses for genuine tripartite nonlocality (GTNL). ...
... Then these linear inequalities' violations serve as device-independent (DI) witnesses for genuine tripartite nonlocality (GTNL). Using estimated measurement-settings-conditional outcome probabilities from a large number of experimental trials implementing a photonic tripartite GHZ protocol, both [28] and [29] claim GTNL by reporting the degree of violation of the DI witnesses in terms of the number of standard deviations (SDs) beyond their maximal value. Both works report a large number of experimental SDs of violation of their respective DI witness. ...
Recent advancements in network nonlocality have led to the concept of local operations and shared randomness-based genuine multipartite nonlocality (LOSR-GMNL). In this paper, we consider two recent experimental demonstrations of LOSR-GMNL, focusing on a tripartite scenario where the goal is to exhibit correlations impossible in a network where each two-party subset shares bipartite resources and every party has access to unlimited shared randomness. Traditional statistical analyses measuring violations of witnessing inequalities by the number of experimental standard deviations do not account for subtleties such as memory effects. We demonstrate a more sound method based on the prediction-based ratio (PBR) protocol to analyse finite experimental data and quantify the strength of evidence in favour of genuine tripartite nonlocality in terms of a valid p-value. In our work, we propose an efficient modification of the test factor optimisation using an approximating polytope approach. By justifying a further restriction to a smaller polytope we enhance practical feasibility while maintaining statistical rigour.
... This approach resolves an anomaly [13] in earlier definitions of the GMNL concept [14,15,16] in which parallel independent two-party nonlocality experiments can be counterintuitively classified as GMNL. The new revised notion of GMNL is named in [17] as LOSR-GMNL, with LOSR standing for local operations and shared randomness; quantum measurements of the three-way entangled GHZ state [18] can exhibit LOSR-GMNL [19,12,13] and recent experiments [1,20,21] provide some initial evidence of the phenomenon. Motivated in part by the LOSR-GMNL definition, this paper studies the general question of how to systematically model n-party conditional distributions, or behaviors, of the form P(A 1 , ..., A n |X 1 , ..., X n ) that are induced as follows: a network of m nonsignaling resources, each shared by a subset of the parties, is measured by the parties in cascaded fashion after each party i receives a setting X i ; then, each party's final outcome A i is a function of the observed outputs from the resources. ...
... The paper concludes with a case study example: inequalities witnessing LOSR-GMNL in the three-party scenario. It is shown that all known three-party inequalities with two settings per party and two outcomes per setting -the simplest possible scenario witnessing LOSR-GMNL (see Section SM 3 of [26]) -can be derived from the inequality of of Mao et al. [1], including the inequality of Chao and Reichardt [19] as formulated in [12], and inequality (1) of Cao et al. [20]. A second inequality of Cao et al., which has an extra setting for one of the parties, can also be derived from that of Mao et al.; a natural open question is whether different inequalities can be discovered in this scenario. ...
... As mentioned earlier, the set of all nonsignaling resource R(a 1 , ..., a n |x 1 , ..., x n ) for a fixed number of parties, inputs, and outputs, comprises a polytope, as it is the set of behaviors satisfying linear equalities (2) along with the linear equalities and inequalities that define valid probability distributions. As such, this polytope will have a certain number N of extreme points R ext i (a 1 , ..., a n |x 1 , ..., x n ), i ∈ {1, ..., N}, for which a general R(a 1 , ..., a n |x 1 , ..., x n ) can be written as a convex combination: R(a 1 , ..., a n |x 1 , ..., x n ) = i p(i)R ext i (a 1 , ..., a n |x 1 , ..., x n ), (19) where p(i) is a probability distribution over the values of i. Employing such an expression for R 1 ( a 1 | x 1 ), we can write P( a 1 , a 2 , ..., a m |x 1 , ..., 20) and the term in brackets in (20) is equal to P i ( a 1 , a 2 , ..., a m |x 1 , ..., x n ), which we define to be the distribution induced when each party uses their original decision with the single change of replacing consultations of R 1 with consultations of R ext i . Hence P is equal to the convex mixture i p(i)P i . ...
This paper examines networks of n measuring parties sharing m independent nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings is causal, supporting the applicability of the inflation technique to constrain such models. For an application, we probe the example of (3,2,2) inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Mao et al. [Phys. Rev. Lett. 129:150401 (2022)]
... In the presence of postselection, one could have selection bias that arises due to conditioning or restricting the data generated in the experiment [47], which might lead to correlations breaking Bell-like inequality without necessarily claiming the genuine LOSR tripartite nonlocality. For example, if we use three independent bipartite-entangled states shared by Alice, Bob, and Charlie, and allow them measuring local parity operators, only postselection on the interested events in the outcomes will lead to the statistics that show genuinely tripartite nonlocal features [48,49]. However, one could potentially close the postselection loophole at the sources by preparing states in a heralded event-ready manner such as using cascaded SPDC sources [19,50] or using on-demand single-photon sources with fusion gates [51] in the future. ...
... Note added.-Recently, we became aware of two similar optical tabletop experimental works without closing locality loopholes [49,52]. ...
Nonlocality captures one of the counterintuitive features of nature that defies classical intuition. Recent investigations reveal that our physical world's nonlocality is at least tripartite; i.e., genuinely tripartite nonlocal correlations in nature cannot be reproduced by any causal theory involving bipartite nonclassical resources and unlimited shared randomness. Here, by allowing the fair sampling assumption and postselection, we experimentally demonstrate such genuine tripartite nonlocality in a network under strict locality constraints that are ensured by spacelike separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole-free violation of the Bell-type inequality by 7.57 standard deviations for a postselected tripartite Greenberger-Horne-Zeilinger state of fidelity (93.13±0.24)%, which convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources with globally shared randomness.
... In the presence of post-selection, one could have selection bias that arises due to conditioning or restricting the data generated in the experiment [46], which might lead to correlations breaking Bell-like inequality without necessarily claiming the genuine LOSR tripartite nonlocality. For example, if we use three independent bipartite entangled states shared by Alice, Bob and Charlie, and allow them measuring local parity operators, only post-selection on the interested events in the outcomes will lead to the statistics that show genuinely tripartite nonlocal features [47,48]. However, one could potentially close the postselection loophole at the sources by preparing states in a heralded event-ready manner such as using cascaded SPDC sources [19,49] or using on-demand single photon sources with fusion gates [50] in the future. ...
... Note added -After finishing our experiment, we became aware of two similar optical tabletop experimental works without closing locality loopholes [48,51]. * These authors contributed equally to this work. ...
Nonlocality captures one of the counter-intuitive features of Nature that defies classical intuition. Recent investigation reveals that our physical world is boundlessly multipartite nonlocal, i.e., there are multipartite correlations in nature that cannot be reproduced by sharing fewer-partite nonlocal resources even with globally shared randomness. Here we report an experimental demonstration of genuine tripartite nonlocality in network under strict locality constraints, which are ensured by space-like separating all relevant events and employing fast quantum random number generators and high-speed polarization measurements. In particular, for a photonic quantum triangular network we observe a locality-loophole free violation of the Bell-type inequality by 7.57 standard deviations for a tripartite GHZ state of fidelity . Our result convincingly disproves the possibility of simulating genuine tripartite nonlocality by bipartite nonlocal resources and unlimited shared randomness, confirming that Nature must be fundamentally boundlessly multipartite.
... In the context of a future quantum internet [4,21], networks connecting multiple stations will play a crucial role. Different topologies have been explored as extensions of the bipartite Bell scenario, ranging from networks with a single source [61][62][63][64] to those involving independent sources [65][66][67][68][69][70]. Our work broadens the study of randomness certification to multipartite networks with hybrid topologies, incorporating both sources of entanglement and quantum channels [33,34,[71][72][73][74]. ...
The certification of randomness is essential for both fundamental science and information technologies. Unlike traditional random number generators, randomness obtained from nonlocal correlations is fundamentally guaranteed to be unpredictable. However, it is also highly susceptible to noise. Here, we show that extending the conventional bipartite Bell scenario to hybrid quantum networks -- which incorporate both quantum channels and entanglement sources -- enhances the robustness of certifiable randomness. Our protocol even enables randomness to be certified from Bell-local states, broadening the range of quantum states useful for this task. Through both theoretical analysis and experimental validation in a photonic network, we demonstrate enhanced performance and improved noise resilience.
... Their validity has been questioned due to selection bias introduced by postselection [57]. However, the generation of multiphoton entangled states in an event-ready manner may pave the way to close the postselection loophole in future experiments [58,59]. While heralded entanglement generation has previously been realized only for bipartite states [60,61], our experiment marks a steady progression towards multipartite systems. ...
Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source ( 547 ± 2 Hz ) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F = 0.7278 ± 0.0106 . Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.
Published by the American Physical Society 2024
... Importantly, the mismatch between classical and quantum causal predictions can be generalized to causal structures beyond that in the paradigmatic Bell scenario. Motivated by the steady progress on quantum networks [13], there have been a number of results [13][14][15][16][17][18][19][20][21] that correlations across the distant parties of causal networks composed of independent sources can also exhibit nonclassical behavior, as already proven in a number of experiments [22][23][24][25][26][27][28]. In particular, quantum networks allow for a novel form of nonlocality that, as opposed to Bell's theorem, does not require the need for measuring different observables [15,18,29]. ...
Seen from the modern lens of causal inference, Bell’s theorem is nothing other than the proof that a specific classical causal model cannot explain quantum correlations. It is thus natural to move beyond Bell’s paradigmatic scenario and consider different causal structures. For the specific case of three observable variables, it is known that there are three nontrivial causal networks. Two of those are known to give rise to quantum nonclassicality: the instrumental and the triangle scenarios. Here we analyze the third and remaining one, which we name the Evans scenario, akin to the causal structure underlying the entanglement-swapping experiment. We prove a number of results about this elusive scenario and introduce new and efficient computational tools for its analysis that can also be adapted to deal with more general causal structures. We do not solve its main open problem—whether quantum nonclassical correlations can arise from it—but give a significant step in this direction by proving that postquantum correlations, analogous to the paradigmatic Popescu-Rohrlich box, do violate the constraints imposed by a classical description of the Evans causal structure.
... If v d has some component orthogonal to that linear span, then the primal formulation in Eq. (11) is infeasible and the dual formulation in Eq. (12) is unbounded. See Appendix B of ref.93 for alternative relaxations of an LP satisfiability problem into an optimization problem, and the connection therein to distance measures such as robustness and nonlocal fraction. Namely, such that 0 n ≤ y d Á M d,n ≤ 1 n : ...
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modeled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity.
... Tripartite behaviors ruling out this class, which can be achieved with appropriate measurements on the three-way entangled GHZ state [11,15], naturally also rule out other definitions with more restrictions on the networks such as a definition disallowing entangled measurements [12], a definition disallowing superquantum bipartite resources [10], or a fourth candidate definition disallowing both. Recent experimental results [15][16][17] provide initial evidence, subject to fair-sampling-type assumptions, for the existence of three-party behaviors that cannot be modeled by even the most general underlying bipartite networks of Ref. [11]. ...
According to recent new definitions, a multi-party behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multi-partite measurement scenario (3 parties, 2 measurement settings, and 2 outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources -- thus witnessing the most general form of GMNL -- but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.
... If v d has some component orthogonal to that linear span, then the primal formulation in Eq. (11) is infeasible and the dual formulation in Eq. (12) is unbounded. See Appendix B of Ref. [85] for alternative relaxations of an LP satisfiability problem into an optimization problem, and the connection therein to distance measures such as robustness and nonlocal fraction. ...
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modelled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity.
... By contrast, our demonstration requires only bipartite sources of entangled states. Notably, bipartite states can be easily prepared with higher coincidence rate and fidelities with respect to the GHZ states [89][90][91][92][93][94][95][96] and thus offer a more scalable platform with the cost of relaxing the simultaneity of events. ...
Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell’s theorem imply new and sometimes stronger forms of nonclassicality. Due to a number of practical difficulties, however, the experimental implementation of such networks remains far less explored. Going beyond what has been previously tested, here we verify the nonlocality of an experimental triangle network, consisting of three independent sources of bipartite entangled photon states interconnecting three distant parties. By performing separable measurements only and evaluating parallel chained Bell inequalities, we show that such networks can lead to a genuine form of tripartite nonlocality, where classical models are unable to mimic the quantum predictions even if some of the parties are allowed to communicate.
... While our experiment presents a test of the genuine multipartite nonlocality, we note that the measurement events of one party are not spacelike separated from those of other parties and the photon detection efficiencies are low; hence, our experiment has the loopholes of locality and fair sampling assumption [3]. The next task along this line of research may be to conduct an experimental test of genuine multipartite nonlocality without these loopholes, like the loophole-free test of Bell inequality [6][7][8][9][10], and a strategy to do so was just proposed in [79]. ...
While Bell nonlocality of a bipartite system is counter-intuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomenss, hence confirming that nature is boundless multipartite nonlocal.
A recent experiment testing the necessity of complex numbers in the standard formulation of quantum theory is recreated using IBM quantum computers. To motivate the experiment, we present a basic construction for real-valued quantum theory. The real-valued description is shown to predict correlations identical to those of complex-valued quantum mechanics for two types of Bell tests based on the Clauser–Horne–Shimony–Holt inequality. A slight modification to one test, however, results in different predictions for the real- and complex-valued constructions. While noisier devices are incapable of delivering convincing results, it is shown that certain devices possess sufficiently small error rates to falsify real-valued formulations of quantum theory for composite states. The results obtained with quantum computers are consistent with published experiments. This work demonstrates the feasibility of using freely available quantum devices to explore foundational features of quantum mechanics with minimal technical expertise. Accordingly, this treatment could inspire novel projects for undergraduate students taking a course on quantum mechanics.
Quantum networks connect and supply a large number of nodes with multi-party quantum resources for secure communication, networked quantum computing and distributed sensing. As these networks grow in size, certification tools will be required to answer questions regarding their properties. In this work we demonstrate a general method to guarantee that certain correlations cannot be generated in a given quantum network. We apply quantum inflation methods to data obtained in quantum group encryption experiments, guaranteeing the impossibility of producing the observed results in networks with fewer optical elements. Our results pave the way for scalable methods of obtaining device-independent guarantees on the network structure underlying multipartite quantum protocols.
Standard procedures for entanglement detection assume that experimenters can exactly implement specific quantum measurements. Here, we depart from such idealizations and investigate, in both theory and experiment, the detection of genuine multipartite entanglement when measurements are subject to small imperfections. For arbitrary qubits number n, we construct multipartite entanglement witnesses where the detrimental influence of the imperfection is independent of n. In a tabletop four-partite photonic experiment, we demonstrate first how a small amount of alignment error can undermine the conclusions drawn from standard entanglement witnesses and then perform the correction analysis. Furthermore, since we consider quantum devices that are trusted but not perfectly controlled, we showcase advantages in terms of noise resilience as compared to device-independent models.
The philosophy of striving for oneness is discussed by considering the three basic questions: What is thinking? Wat is space-time? What is life-death? in Part One, and comments on the maxims of the Svabhavikasutra, the antecedent of the Bhagavadgita, in Part Two. The book has a bibliography and an index.
The book emphasizes that opposites are mutually created only together with their difference, indicating that existence in inherently triune and paradoxical, similar to the singlet state in quantum mechanics. Without a distinction there is no existence. Time and space are shown to be illusionary and discrete. References to recent research in physics and cosmology are given.
Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein's belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell correlation depth can be certified from experimental data. As an illustrating example, we variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide towards exploiting multipartite Bell correlation in a wide spectrum of practical applications.
We review methods that allow one to detect and characterise quantum correlations in many-body systems, with a special focus on approaches which are scalable. Namely, those applicable to systems with many degrees of freedom, without requiring a number of measurements or computational resources to analyze the data that scale exponentially with the system size. We begin with introducing the concepts of quantum entanglement, Einstein-Podolsky-Rosen steering, and Bell nonlocality in the bipartite scenario, to then present their multipartite generalisation. We review recent progress on characterizing these quantum correlations from partial information on the system state, such as through data-driven methods or witnesses based on low-order moments of collective observables. We then review state-of-the-art experiments that demonstrated the preparation, manipulation and detection of highly-entangled many-body systems. For each platform (e.g. atoms, ions, photons, superconducting circuits) we illustrate the available toolbox for state preparation and measurement, emphasizing the challenges that each system poses. To conclude, we present a list of timely open problems in the field.
According to recent new definitions, a multiparty behavior is genuinely multipartite nonlocal (GMNL) if it cannot be modeled by measurements on an underlying network of bipartite-only nonlocal resources, possibly supplemented with local (classical) resources shared by all parties. The new definitions differ on whether to allow entangled measurements upon, and/or superquantum behaviors among, the underlying bipartite resources. Here, we categorize the full hierarchy of these new candidate definitions of GMNL in three-party quantum networks, highlighting the intimate link to device-independent witnesses of network effects. A key finding is the existence of a behavior in the simplest nontrivial multipartite measurement scenario (three parties, two measurement settings, and two outcomes) that cannot be simulated in a bipartite network prohibiting entangled measurements and superquantum resources—thus witnessing the most general form of GMNL—but can be simulated with bipartite-only quantum states with an entangled measurement, indicating an approach to device-independent certification of entangled measurements with fewer settings than in previous protocols. Surprisingly, we also find that this (3,2,2) behavior, as well as the others previously studied as device-independent witnesses of entangled measurements, can all be simulated at a higher echelon of the GMNL hierarchy that allows superquantum bipartite resources while still prohibiting entangled measurements. This poses a challenge to a theory-independent understanding of entangled measurements as an observable phenomenon distinct from bipartite nonlocality.
Genuine multipartite nonlocality constitutes the strongest form of nonlocality, which is a key resource for many quantum communication and computational tasks. Standard methods for certifying nonlocality often require accessing contradictions in paradoxes or violations of Bell inequalities for composite quantum systems. However, the existing approaches become infeasible and cannot be adopted straightforwardly for a quantum network scenario, which usually possesses complex topological structure and many independent quantum sources. We have developed a simple and customizable strategy to achieve scalable, efficient, and flexible characterizations for various typical quantum network scenarios. The subtle something-versus-nothing contradiction in Hardy-type paradoxes without inequality allows us to substantiate genuine multipartite nonlocality in general quantum networks. Examples range from chain-type network to star-type network, with source connections of any pure entangled permutation symmetric multiqubit states, entangled two-qubit states, etc. The tools extend significantly our ability to certify genuine multipartite nonlocality in state-of-the-art network situations, and make a prominent step forward toward deeper understanding and practical depiction of quantum networks.
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.
There are multipartite entangled states in many-body systems which may be potential resources in various quantum applications. In this paper, based on clustering theorems, we show that both the gapped ground state and thermal state at an upper-bounded inverse temperature have no genuine multipartite nonlocality when disjoint regions are far away from each other. The present n-particle system shows only biseparable quantum correlations when the propagation relations show exponential decay. Similar result holds for spin systems with product states as initial states. These results show interesting features of quantum many-body systems with exponential decay of correlations.
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.
Bell’s theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell’s theorem to consider more sophisticated experiments that involve several independent sources that distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.
We introduce the class of genuinely local operations and shared randomness multipartite nonlocal correlations, that is, correlations between N parties that cannot be obtained from unlimited shared randomness supplemented by any composition of (N−1)-shared causal generalized probabilistic theory (GPT) resources. We then show that noisy N-partite Greenberger-Horne-Zeilinger (GHZ) quantum states as well as the three-partite W quantum state can produce such correlations. This proves, if the operational predictions of quantum theory are correct, that nature's nonlocality must be boundlessly multipartite in any causal GPT. We develop a computational method which certifies that a noisy N=3 GHZ quantum state with fidelity 85% satisfies this property, making an experimental demonstration of our results within reach. We provide our definition and contrast it with preexisting notions of genuine multipartite nonlocality. This work extends a more compact parallel Letter [X. Coiteux-Roy et al., No Bipartite-Nonlocal Causal Theory Can Explain Nature's Correlations, Phys. Rev. Lett. 127, 200401 (2021)] on the same subject and provides all the required technical proofs.
The standard definition of genuine multipartite entanglement stems from the need to assess the quantum control over an ever-growing number of quantum systems. We argue that this notion is easy to hack: in fact, a source capable of distributing bipartite entanglement can, by itself, generate genuine k-partite entangled states for any k. We propose an alternative definition for genuine multipartite entanglement, whereby a quantum state is genuinely network k-entangled if it cannot be produced by applying local trace-preserving maps over several (k−1)-partite states distributed among the parties, even with the aid of global shared randomness. We provide analytic and numerical witnesses of genuine network entanglement, and we reinterpret many past quantum experiments as demonstrations of this feature.
Contrary to the usual assumption of at least partial control of quantum dynamics, a surprising recent result proved that an arbitrary quantum state can be probabilistically reset to a state in the past by having it interact with probing systems in a consistent but uncontrolled way. We present a photonic implementation to achieve this resetting process, experimentally verifying that a state can be probabilistically reset to its past with a fidelity of 0.870 ± 0.012 . We further demonstrate the preservation of an entangled state, which still violates a Bell inequality, after half of the entangled pair was reset. The ability to reset uncontrolled quantum states has implications in the foundations of quantum physics and applications in areas of quantum technology.
The possibility of Bell inequality violations in quantum theory had a profound impact on our understanding of the correlations that can be shared by distant parties. Generalizing the concept of Bell nonlocality to networks leads to novel forms of correlations, the characterization of which is, however, challenging. Here, we investigate constraints on correlations in networks under the natural assumptions of no-signaling and independence of the sources. We consider the triangle network with binary outputs, and derive strong constraints on correlations even though the parties receive no input, i.e., each party performs a fixed measurement. We show that some of these constraints are tight, by constructing explicit local models (i.e. where sources distribute classical variables) that can saturate them. However, we also observe that other constraints can apparently not be saturated by local models, which opens the possibility of having nonlocal (but non-signaling) correlations in the triangle network with binary outputs.
Quantum systems can be exploited for disruptive technologies but in practice quantum features are fragile due to noisy environments. Quantum coherence, a fundamental such feature, is a basis-dependent property that is known to exhibit a resilience to certain types of Markovian noise. Yet, it is still unclear whether this resilience can be relevant in practical tasks. Here, we experimentally investigate the resilient effect of quantum coherence in a photonic Greenberger-Horne-Zeilinger state under Markovian bit-flip noise, and explore its applications in a noisy metrology scenario. In particular, using up to six-qubit probes, we demonstrate that the standard quantum limit can be outperformed under a transversal noise strength of approximately equal magnitude to the signal, providing experimental evidence of metrological advantage even in the presence of uncorrelated Markovian noise. This work highlights the important role of passive control in noisy quantum hardware, which can act as a low-overhead complement to more traditional approaches such as quantum error correction, thus impacting on the deployment of quantum technologies in real-world settings.
Quantum networks allow in principle for completely novel forms of quantum correlations. In particular, quantum nonlocality can be demonstrated here without the need of having various input settings, but only by considering the joint statistics of fixed local measurement outputs. However, previous examples of this intriguing phenomenon all appear to stem directly from the usual form of quantum nonlocality, namely via the violation of a standard Bell inequality. Here we present novel examples of “quantum nonlocality without inputs,” which we believe represent a new form of quantum nonlocality, genuine to networks. Our simplest examples, for the triangle network, involve both entangled states and joint entangled measurements. A generalization to any odd-cycle network is also presented.
Inspired by the recent remarkable progress in the experimental test of local realism, we report here such a test that achieves an efficiency greater than (78%)2 for entangled photon pairs separated by 183 m. Further utilizing the randomness in cosmic photons from pairs of stars on the opposite sides of the sky for the measurement setting choices, we not only close the locality and detection loopholes simultaneously, but also test the null hypothesis against local hidden variable mechanisms for events that took place 11 years ago (13 orders of magnitude longer than previous experiments). After considering the bias in measurement setting choices, we obtain an upper bound on the p value of 7.87×10−4, which clearly indicates the rejection with high confidence of potential local hidden variable models. One may further push the time constraint on local hidden variable mechanisms deep into the cosmic history by taking advantage of the randomness in photon emissions from quasars with large aperture telescopes.
This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the Universe, serving as a clock, being in a state corresponding to a time t. Doing so assigns a conditional state to the rest of the Universe , referred to as the system. We demonstrate that when the total Hamiltonian appearing in the Wheeler-DeWitt equation contains an interaction term coupling the clock and system, the conditional state satisfies a time-nonlocal Schr\"{o}dinger equation in which the system Hamiltonian is replaced with a self-adjoint integral operator.
An experimental test of Bell's inequality allows to rule out any local-realistic description of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of space-like separation between the measurement events. Only very recently both loopholes could be closed simultaneously. Here we present an event-ready loophole-free test based on combining heralded entanglement of atoms separated by 398 m with fast and efficient measurements of the atomic spin states. We obtain a violation of (compared to the maximal value of 2 achievable with local-hidden variable models) which allows us to refute the hypothesis of local-realism with a significance level .
The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the structure includes latent variables. We here introduce the inflation technique for tackling this problem. An inflation of a causal structure is a new causal structure that can contain multiple copies of each of the original variables, but where the ancestry of each copy mirrors that of the original. For every distribution compatible with the original causal structure we identify a corresponding family of distributions, over certain subsets of inflation variables, which is compatible with the inflation structure. It follows that compatibility constraints at the inflation level can be translated to compatibility constraints at the level of the original causal structure; even if the former are weak, such as observable statistical independences implied by disjoint causal ancestry, the translated constraints can be strong. In particular, we can derive inequalities whose violation by a distribution witnesses that distribution's incompatibility with the causal structure (of which Bell inequalities and Pearl's instrumental inequality are prominent examples). We describe an algorithm for deriving all of the inequalities for the original causal structure that follow from ancestral independences in the inflation. Applied to an inflation of the Triangle scenario with binary variables, it yields inequalities that are stronger in at least some aspects than those obtainable by existing methods. We also describe an algorithm that derives a weaker set of inequalities but is much more efficient. Finally, we discuss which inflations
Quantum entanglement among multiple spatially separated particles is of fundamental interest, and can serve as central resources for studies in quantum nonlocality, quantum-to-classical transition, quantum error correction, and quantum simulation. The ability of generating an increasing number of entangled particles is an important benchmark for quantum information processing. The largest entangled states were previously created with fourteen trapped ions, eight photons, and five superconducting qubits. Here, based on spontaneous parametric down-converted two-photon entanglement source with simultaneously a high brightness of ~12 MHz/W, a collection efficiency of ~70% and an indistinguishability of ~91% between independent photons, we demonstrate, for the first time, genuine and distillable entanglement of ten single photons under different pump power. Our work creates a state-of-the-art platform for multi-photon experiments, and provide enabling technologies for challenging optical quantum information tasks such as high-efficiency scattershot boson sampling with many photons.
Quantum nonlocality gives us deeper insight into quantum physics. In addition, quantum nonlocality has been further recognized as an essential resource for device-independent quantum information processing in recent years. Most experiments of nonlocality are performed using a photonic system. However, until now, photonic experiments of nonlocality have involved at most four photons. Here, for the first time, we experimentally demonstrate the six-photon quantum nonlocality in an all-versus-nothing manner based on a high-fidelity (88.4%) six-photon Greenberger-Horne-Zeilinger state. Our experiment pushes multiphoton nonlocality studies forward to the six-photon region and might provide a larger photonic system for device-independent quantum information protocols.
We present a loophole-free violation of local realism using entangled photon
pairs. We ensure that all relevant events in our Bell test are spacelike
separated by placing the parties far enough apart and by using fast random
number generators and high-speed polarization measurements. A high-quality
polarization-entangled source of photons, combined with high-efficiency,
low-noise, single-photon detectors, allows us to make measurements without
requiring any fair-sampling assumptions. Using a hypothesis test, we compute
p-values as small as for our Bell violation while
maintaining the spacelike separation of our events. We estimate the degree to
which a local realistic system could predict our measurement choices.
Accounting for this predictability, our smallest adjusted p-value is . We therefore reject the hypothesis that local realism governs
our experiment.
Local realism is the worldview in which physical properties of objects exist
independently of measurement and where physical influences cannot travel faster
than the speed of light. Bell's theorem states that this worldview is
incompatible with the predictions of quantum mechanics, as is expressed in
Bell's inequalities. Previous experiments convincingly supported the quantum
predictions. Yet, every experiment performed to date required assumptions that
provide loopholes for a local realist explanation. Here we report a Bell test
that closes the most significant of these loopholes simultaneously. Using a
well-optimized source of entangled photons, rapid setting generation, and
highly efficient superconducting detectors, we observe a violation of a Bell
inequality with high statistical significance.
Non-classical states of light are of fundamental importance for emerging
quantum technologies. All optics experiments producing multi-qubit entangled
states have until now relied on outcome post-selection, a procedure where only
the measurement results corresponding to the desired state are considered. This
method severely limits the usefulness of the resulting entangled states. Here,
we show the direct production of polarization-entangled photon triplets by
cascading two entangled downconversion processes. Detecting the triplets with
high efficiency superconducting nanowire single-photon detectors allows us to
fully characterize them through quantum state tomography. We use our
three-photon entangled state to demonstrate the ability to herald Bell states,
a task which was not possible with previous three-photon states, and test local
realism by violating the Mermin and Svetlichny inequalities. These results
represent a significant breakthrough for entangled multi-photon state
production by eliminating the constraints of outcome post-selection, providing
a novel resource for optical quantum information processing.
Quantum correlations, often observed as violations of Bell inequalities, are critical to our understanding of the quantum world, with far-reaching technological and fundamental impact. Many tests of Bell inequalities have studied pairs of correlated particles. However, interest in multi-particle quantum correlations is driving the experimental frontier to test larger systems. All violations to date require supplementary assumptions that open results to loopholes, the closing of which is one of the most important challenges in quantum science. Seminal experiments have closed some loopholes, but no experiment has closed locality loopholes with three or more particles. Here, we close both the locality and freedom-of-choice loopholes by distributing three-photon Greenberger–Horne–Zeilinger entangled states to independent observers. We measured a violation of Mermin's inequality18 with parameter 2.77 ± 0.08, violating its classical bound by nine standard deviations. These results are a milestone in multi-party quantum communication and a significant advancement of the foundations of quantum mechanics.
We have measured the linear polarization correlation of the photons emitted in an atomic cascade of calcium. It has been shown by a generalization of Bell's inequality that the existence of local hidden variables imposes restrictions on this correlation in conflict with the predictions of quantum mechanics. Our data, in agreement with quantum mechanics, violate these restrictions to high statistical accuracy, thus providing strong evidence against local hidden-variable theories.
Physical principles constrain the way nonlocal correlations can be
distributed among parties in a Bell experiment. Here, we show that in any
no-signalling theory the amount of violation of a certain class of Bell
inequalities tightly bounds the knowledge that an external observer can gain
about outcomes of any single measurement performed by the parties. Analogous
relations are then proved for quantum correlations in the simplest scenario of
three parties performing two dichotomic measurements. Later, we relate these
monogamy trade-offs to the generation and amplification of randomness, in the
latter case, in particular, reproducing and generalizing the results of [R.
Colbeck and R. Renner, Nature Phys. 8, 450 (2012)]. Finally, we show that with
the aid of the chained Bell inequalities one can amplify the epsilon-sources
for epsilon<1/6, improving the existing results.
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. Many quantum phenomena are found to have analogues within this toy theory. These include the noncommutativity of measurements, interference, the multiplicity of convex decompositions of a mixed state, the impossibility of discriminating nonorthogonal states, the impossibility of a universal state inverter, the distinction between bipartite and tripartite entanglement, the monogamy of pure entanglement, no cloning, no broadcasting, remote steering, teleportation, entanglement swapping, dense coding, mutually unbiased bases, and many others. The diversity and quality of these analogies is taken as evidence for the view that quantum states are states of incomplete knowledge rather than states of reality. A consideration of the phenomena that the toy theory fails to reproduce, notably, violations of Bell inequalities and the existence of a Kochen-Specker theorem, provides clues for how to proceed with this research program.
We review and develop an algorithm to determine arbitrary quantum bounds based on the seminal work of Tsirelson [ Lett. Math. Phys. 4 93 (1980)]. The potential of this algorithm is demonstrated by both deriving marginal-involving number-valued quantum bounds and identifying a generalized class of function-valued quantum bounds. Those results facilitate an eight-dimensional volume analysis of quantum mechanics which extends the work of Cabello [ Phys. Rev. A 72 012113 (2005)]. We contrast the quantum volume defined by these bounds to that of macroscopic locality, defined by the inequalities corresponding to the first level of the hierarchy of Navascués et al. [ New J. Phys. 10 073013 (2008)], proving our function-valued quantum bounds to be more complete.
A theorem of Bell, proving that certain predictions of quantum mechanics are inconsistent with the entire family of local hidden-variable theories, is generalized so as to apply to realizable experiments. A proposed extension of the experiment of Kocher and Commins, on the polarization correlation of a pair of optical photons, will provide a decisive test between quantum mechanics and local hidden-variable theories.
Bell's Theorem witnesses that the predictions of quantum theory cannot be
reproduced by theories of local hidden variables in which observers can choose
their measurements independently of the source. Working out an idea of
Branciard, Rosset, Gisin and Pironio, we consider scenarios which feature
several sources, but no choice of measurement for the observers. Every Bell
scenario can be mapped into such a \emph{correlation scenario}, and Bell's
Theorem then discards those local hidden variable theories in which the sources
are independent. However, most correlation scenarios do not arise from Bell
scenarios, and we describe examples of (quantum) nonlocality in some of these
scenarios, while posing many open problems along the way. Some of our scenarios
have been considered before by mathematicians in the context of causal
inference.
A Franson-type test of Bell inequalities by photons 10.9 km apart is presented. Energy-time entangled photon-pairs are measured using two-channel analyzers, leading to a violation of the inequalities by 16 standard deviations without subtracting accidental coincidences. Subtracting them, a 2-photon interference visibility of 95.5% is observed, demonstrating that distances up to 10 km have no significant effect on entanglement. This sets quantum cryptography with photon pairs as a practical competitor to the schemes based on weak pulses. Comment: 4 pages, REVTeX, 2 postscript figures included
We point out a loophole problem in some recent experimental claims to produce three-particle entanglement. The problem consists in the question whether mixtures of two-particle entangled states might suffice to explain the experimental data. In an attempt to close this loophole, we review two sufficient conditions that distinguish between N-particle states in which all N particles are entangled to each other and states in which only M particles are entangled (with M<N). It is shown that three recent experiments to obtain three-particle entangled states (Bouwmeester et al., Pan et al., and Rauschenbeutel et al.) do not meet these conditions. We conclude that the question whether these experiments provide confirmation of three-particle entanglement remains unresolved. We also propose modifications of the experiments that would make such confirmation feasible.
An inexhaustive review of Hawking radiation and black hole thermodynamics is given, focusing especially upon some of the historical aspects as seen from the biased viewpoint of a minor player in the field on and off for the past thirty years. Comment: 46 pages, LaTeX, review article solicited for a celebratory Focus Issue on Relativity, ``Spacetime 100 Years Later,'' to be published in New Journal of Physics. A new paragraph was added after Eq. (2), and a new long Section 5 on "Logarithmic corrections to black hole entropy."
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.
Nonlocal boxes are conceptual tools that capture the essence of the phenomenon of quantum nonlocality, central to modern quantum theory and quantum technologies. We introduce network nonlocal boxes tailored for quantum networks under the natural assumption that these networks connect independent sources and do not allow signaling. Hence, these boxes satisfy the no-signaling and independence principle. For the case of boxes without inputs, connecting pairs of bipartite sources and producing binary outputs, we prove that the sources and boxes producing local random outputs and maximal two-box correlations, i.e., E2=2−1, E2o=1, are essentially unique.
We show that some tripartite quantum correlations are inexplicable by any causal theory involving bipartite nonclassical common causes and unlimited shared randomness. This constitutes a device-independent proof that nature's nonlocality is fundamentally at least tripartite in every conceivable physical theory-no matter how exotic. To formalize this claim, we are compelled to substitute Svetlichny's historical definition of genuine tripartite nonlocality with a novel theory-agnostic definition tied to the framework of local operations and shared randomness. A companion article by Coiteux-Roy et al. generalizes these concepts to any N≥3 number of parties, providing experimentally amenable device-independent inequality constraints along with quantum correlations violating them, thereby certifying that nature's nonlocality must be boundlessly multipartite.
Parties connected to independent sources through a network can generate correlations among themselves. Notably, the space of feasible correlations for a given network, depends on the physical nature of the sources and the measurements performed by the parties. In particular, quantum sources give access to nonlocal correlations that cannot be generated classically. In this paper, we derive a universal limit on correlations in networks in terms of their covariance matrix. We show that in a network satisfying a certain condition, the covariance matrix of any feasible correlation can be decomposed as a summation of positive semidefinite matrices each of whose terms corresponds to a source in the network. Our result is universal in the sense that it holds in
any
physical theory of correlation in networks, including the classical, quantum and all generalized probabilistic theories.
Quantum entanglement and nonlocality are inextricably linked. However, while entanglement is necessary for nonlocality, it is not always sufficient in the standard Bell scenario. We derive sufficient conditions for entanglement to give rise to genuine multipartite nonlocality in networks. We find that any network where the parties are connected by bipartite pure entangled states is genuine multipartite nonlocal, independently of the amount of entanglement in the shared states and of the topology of the network. As an application of this result, we also show that all pure genuine multipartite entangled states are genuine multipartite nonlocal in the sense that measurements can be found on finitely many copies of any genuine multipartite entangled state to yield a genuine multipartite nonlocal behavior. Our results pave the way toward feasible manners of generating genuine multipartite nonlocality using any connected network.
More than 50 years ago, John Bell proved that no theory of nature that obeys locality and realism can reproduce all the predictions of quantum theory: in any local-realist theory, the correlations between outcomes of measurements on distant particles satisfy an inequality that can be violated if the particles are entangled. Numerous Bell inequality tests have been reported; however, all experiments reported so far required additional assumptions to obtain a contradiction with local realism, resulting in 'loopholes'. Here we report a Bell experiment that is free of any such additional assumption and thus directly tests the principles underlying Bell's inequality. We use an event-ready scheme that enables the generation of robust entanglement between distant electron spins (estimated state fidelity of 0.92 ± 0.03). Efficient spin read-out avoids the fair-sampling assumption (detection loophole), while the use of fast random-basis selection and spin read-out combined with a spatial separation of 1.3 kilometres ensure the required locality conditions. We performed 245 trials that tested the CHSH-Bell inequality S ≤ 2 and found S = 2.42 ± 0.20 (where S quantifies the correlation between measurement outcomes). A null-hypothesis test yields a probability of at most P = 0.039 that a local-realist model for space-like separated sites could produce data with a violation at least as large as we observe, even when allowing for memory in the devices. Our data hence imply statistically significant rejection of the local-realist null hypothesis. This conclusion may be further consolidated in future experiments; for instance, reaching a value of P = 0.001 would require approximately 700 trials for an observed S = 2.4. With improvements, our experiment could be used for testing less-conventional theories, and for implementing device-independent quantum-secure communication and randomness certification.
It is demonstrated that the premisses of the Einstein-Podolsky-Rosen
paper are inconsistent when applied to quantum systems consisting of at
least three particles. The demonstration reveals that the EPR program
contradicts quantum mechanics even for the cases of perfect
correlations. By perfect correlations is meant arrangements by which the
result of the measurement on one particle can be predicted with
certainty given the outcomes of measurements on the other particles of
the system. This incompatibility with quantum mechanics is stronger than
the one previously revealed for two-particle systems by Bell's
inequality, where no contradiction arises at the level of perfect
correlations. Both spin-correlation and multiparticle interferometry
examples are given of suitable three- and four-particle arrangements,
both at the gedanken and at the real experiment level.
The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. It is urged that in further examination of this problem an interesting axiom would be that mutually distant systems are independent of one another.
Bell's 1964 theorem, which states that the predictions of quantum theory
cannot be accounted for by any local theory, represents one of the most
profound developments in the foundations of physics. In the last two decades,
Bell's theorem has been a central theme of research from a variety of
perspectives, mainly motivated by quantum information science, where the
nonlocality of quantum theory underpins many of the advantages afforded by a
quantum processing of information. The focus of this review is to a large
extent oriented by these later developments. We review the main concepts and
tools which have been developed to describe and study the nonlocality of
quantum theory, and which have raised this topic to the status of a full
sub-field of quantum information science.
It is well known that measurements performed on spatially separated entangled quantum systems can give rise to correlations that are nonlocal, in the sense that a Bell inequality is violated. They cannot, however, be used for superluminal signaling. It is also known that it is possible to write down sets of “superquantum” correlations that are more nonlocal than is allowed by quantum mechanics, yet are still nonsignaling. Viewed as an information-theoretic resource, superquantum correlations are very powerful at reducing the amount of communication needed for distributed computational tasks. An intriguing question is why quantum mechanics does not allow these more powerful correlations. We aim to shed light on the range of quantum possibilities by placing them within a wider context. With this in mind, we investigate the set of correlations that are constrained only by the no-signaling principle. These correlations form a polytope, which contains the quantum correlations as a (proper) subset. We determine the vertices of the no-signaling polytope in the case that two observers each choose from two possible measurements with d outcomes. We then consider how interconversions between different sorts of correlations may be achieved. Finally, we consider some multipartite examples.
We have measured the linear polarization correlation of the photons emitted in a radiative atomic cascade of calcium. A high-efficiency source provided an improved statistical accuracy and an ability to perform new tests. Our results, in excellent agreement with the quantum mechanical predictions, strongly violate the generalized Bell's inequalities, and rule out the whole class of realistic local theories. No significant change in results was observed with source-polarizer separations of up to 6.5 m.
In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a theorem. Nonlocal superquantum correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.
Due to the importance of entanglement for quantum information purposes, a
framework has been developed for its characterization and quantification as a
resource based on the following operational principle: entanglement among N
parties cannot be created by local operations and classical communication, even
when parties collaborate. More recently, nonlocality has been identified
as another resource, alternative to entanglement and necessary for
device-independent quantum information protocols. We introduce an operational
framework for nonlocality based on a similar principle: nonlocality among N
parties cannot be created by local operations and allowed classical
communication even when parties collaborate. We then show that the
standard definition of multipartite nonlocality, due to Svetlichny, is
inconsistent with this operational approach: according to it, genuine
tripartite nonlocality could be created by two collaborating parties. We
finally discuss alternative definitions for which consistency is recovered.
Quantum systems that have never interacted can become nonlocally correlated through a process called entanglement swapping. To characterize nonlocality in this context, we introduce local models where quantum systems that are initially uncorrelated are described by uncorrelated local variables. This additional assumption leads to stronger tests of nonlocality. We show, in particular, that an entangled pair generated through entanglement swapping will already violate a Bell-type inequality for visibilities as low as 50% under our assumption.
We derive an inequality, violated by quantum mechanics, that in a three-body system can detect three-body correlations that cannot be reduced to mixtures of two-body ones related locally to the third body.
The problem of reconciling general relativity and quantum theory
has fascinated and bedeviled physicists for more than 70 years.
Despite recent progress in string theory and loop quantum
gravity, a complete solution remains out of reach. I review the
status of the continuing effort to quantize gravity,
emphasizing the underlying conceptual issues and the various
attempts to come to grips with them.