Elie Wolfe

Perimeter Institute

Separability criteria are typically of the necessary, but not sufficient, variety, in that satisfying some separability criterion, such as positivity of eigenvalues under partial transpose, does not strictly imply separability. Certifying separability amounts to proving the existence of a decomposition of a target mixed state into some convex combi...

Analytic Maximazation of arbitrary Local Measurement Operators, and Tsirelson Inequalities [Note: recipient of "Best Poster" award]

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 facili...

Nonclassical causal modeling was developed in order to explain violations of Bell inequalities while adhering to relativistic causal structure and f a i t h f u l n e s s ---that is, avoiding fine-tuned causal explanations. Recently, a no-go theorem that can be viewed as being stronger than Bell's theorem has been derived, based on extensions of th...

What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simpl...

The possibility of nonclassicality in networks unrelated to Bell's original eponymous theorem has recently attracted significant interest. Here, we identify a sufficient condition for being "outside the shadow of Bell's theorem" and introduce a testable criterion capable of certifying the novelty of instances of network-nonclassicality which we cal...

Bell's theorem, a cornerstone of quantum theory, shows that quantum correlations are incompatible with a classical theory of cause and effect. Through the lens of causal inference, it can be understood as a particular case of causal compatibility, which delves into the alignment of observational data with a given causal structure. Here, we explore...

From the modern perspective of causal inference, Bell's theorem -- a fundamental signature of quantum theory -- is a particular case where quantum correlations are incompatible with the classical theory of causality, and the generalization of Bell's theorem to quantum networks has led to several breakthrough results and novel applications. Here, we...

The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independencies) as well as inequality constraints (Instrumental and Bell inequalities being prototypical examples) on their compatible distribution over the observed variables. Enumerating a causal st...

A well-motivated method for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here formulate this problem as a linear program and provide an open-source implementation of it which tests whether or not any given prepare-measure experiment is classically explaina...

A standard approach to quantifying resources is to determine which operations on the resources are freely available, and to deduce the partial order over resources that is induced by the relation of convertibility under the free operations. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, i.e., e n...

The classical causal relations between a set of variables, some observed and some latent, can induce both equality constraints (typically conditional independences) as well as inequality constraints (Instrumental and Bell inequalities being prototypical examples) on their compatible distribution over the observed variables. Enumerating a causal str...

The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particu...

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable notion of cla...

We introduce Inflation, a Python library for assessing whether an observed probability distribution is compatible with a causal explanation. This is a central problem in both theoretical and applied sciences, which has recently witnessed significant advances from the area of quantum nonlocality, namely, in the development of inflation techniques. I...

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 n...

We implement triangle causal structures in photonics platforms and detect different forms of nonlocality. In particular, we focused on the Genuine Multipartite Non-locality and on the nonlocality exhibited in a network without freedom of choice.

Recently there has been interest, and impressive progress, in extending the definition of contextuality to systems with disturbance. We prove here that such an endeavor cannot simultaneously satisfy the following core principles of contextuality: (1) Measuring more information cannot change a contextual system to a noncontextual one. (2) Classical...

We introduce Inflation, a Python library for assessing whether an observed probability distribution is compatible with a causal explanation. This is a central problem in both theoretical and applied sciences, which has recently witnessed important advances from the area of quantum nonlocality, namely, in the development of inflation techniques. Inf...

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...

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 tripart...

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 fo...

The gold standard for demonstrating that an experiment resists any classical explanation is to show that its statistics violate generalized noncontextuality. We here provide an open-source linear program for testing whether or not any given prepare-measure experiment is classically-explainable in this sense. The input to the program is simply an ar...

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 fo...

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 $\left|{GHZ}_3\right\rangle=(\left|000\right\rangle+\...

The formalism of generalized probabilistic theories (GPTs) was originally developed as a way to characterize the landscape of conceivable physical theories. Thus, the GPT describing a given physical theory necessarily includes all physically possible processes. We here consider the question of how to provide a GPT-like characterization of a particu...

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 Gre...

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 thi...

Bell’s theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classi...

Causal models with unobserved variables impose nontrivial constraints on the distributions over the observed variables. When a common cause of two variables is unobserved, it is impossible to uncover the causal relation between them without making additional assumptions about the model. In this work, we consider causal models with a promise that un...

Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by $e$-se...

The existence of incompatible measurements is often believed to be a feature of quantum theory which signals its inconsistency with any classical worldview. To prove the failure of classicality in the sense of Kochen-Specker noncontextuality, one does indeed require sets of incompatible measurements. However, a more broadly applicable and more perm...

Causality is a seminal concept in science: Any research discipline, from sociology and medicine to physics and chemistry, aims at understanding the causes that could explain the correlations observed among some measured variables. While several methods exist to characterize classical causal models, no general construction is known for the quantum c...

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 t...

We introduce the class of Genuinely Local Operation and Shared Randomness (LOSR) 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-parti...

Bell's theorem is typically understood as the proof that quantum theory is incompatible with local hidden variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum correlations with classical causal models. The violation of a Bell inequality, however, does not exclude classi...

To make precise the sense in which the operational predictions of quantum theory conflict with a classical worldview, it is necessary to articulate a notion of classicality within an operational framework. A widely applicable notion of classicality of this sort is whether or not the predictions of a given operational theory can be explained by a ge...

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 a...

The causal compatibility question asks whether a given causal structure graph — possibly involving latent variables — constitutes a genuinely plausible causal explanation for a given probability distribution over the graph’s observed categorical variables. Algorithms predicated on merely necessary constraints for causal compatibility typically suff...

We take a resource-theoretic approach to the problem of quantifying nonclassicality in Bell scenarios. The resources are conceptualized as probabilistic processes from the setting variables to the outcome variables having a particular causal structure, namely, one wherein the wings are only connected by a common cause. We term them "common-cause bo...

A standard approach to quantifying resources is to determine which operations on the resources are freely available and to deduce the ordering relation among the resources that these operations induce. If the resource of interest is the nonclassicality of the correlations embodied in a quantum state, that is, entanglement, then it is typically pres...

Some properties of physical systems can be characterized from their correlations. In that framework, subsystems are viewed as abstract devices that receive measurement settings as inputs and produce measurement outcomes as outputs. The labeling convention used to describe these inputs and outputs does not affect the physics; and relabelings are eas...

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 propo...

One of the most well-motivated and widely applicable notions of classicality for an operational theory is explainability by a generalized-noncontextual ontological model. We here explore what notion of classicality this implies for the generalized probabilistic theory (GPT) that arises from a given operational theory, focusing on prepare-and-measur...

Causality is a seminal concept in science: any research discipline, from sociology and medicine to physics and chemistry, aims at understanding the causes that could explain the correlations observed among some measured variables. While several methods exist to characterize classical causal models, no general construction is known for the quantum c...

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...

A Bell experiment can be conceptualized as a box, i.e., a process taking classical setting variables to classical outcome variables, which has a common-cause structure, i.e., one that can be realized by implementing local measurements on systems that are prepared by a common-cause mechanism, with no cause-effect relations across the wings of the ex...

Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how two contextuality scenarios combine into a joint one. Under the premise that the the allowed probabilistic models sa...

The causal structure of any experiment implies restrictions on the observable correlations between measurement outcomes, which are different for experiments exploiting classical, quantum, or post-quantum resources. In the study of Bell nonlocality, these differences have been explored in great detail for more and more involved causal structures. He...

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not...

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability implies global joint measurability for sharp measurements [vimeo.com/52923835 (2009)]. To date, it seemed that Specker's principle failed to single out quantum theory from the space of all general probabilistic theo...

Ernst Specker considered a particular feature of quantum theory to be especially fundamental, namely that pairwise joint measurability of sharp measurements implies their global joint measurability (https://vimeo.com/52923835). To date, Specker's principle seemed incapable of singling out quantum theory from the space of all general probabilistic t...

When a measurement is compatible with each of two other measurements that are incompatible with one another, these define distinct contexts for the given measurement. The Kochen-Specker theorem rules out models of quantum theory that satisfy a particular assumption of context-independence: that sharp measurements are assigned outcomes both determin...

Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of which has a finite number of outcomes. Given any fixed sets of operational equivalences among the preparation...

Within the framework of generalized noncontextuality, we introduce a general technique for systematically deriving noncontextuality inequalities for any experiment involving finitely many preparations and finitely many measurements, each of which has a finite number of outcomes. Given any fixed sets of operational equivalences among the preparation...

It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not...

It has long been recognized that certain quantum correlations are incompatible with particular assumption about classical causal structure. Given a causal structure of unknown classicality, the presence of such correlations certifies the non-classical nature of the causal structure in a device independent fashion. In structures where all parties sh...

We present an algebraic description of the sets of local correlations in arbitrary networks, when the parties have finite inputs and outputs. We consider networks generalizing the usual Bell scenarios by the presence of multiple uncorrelated sources. We prove a finite upper bound on the cardinality of the value sets of the local hidden variables. C...

The causal inference problem consists in determining whether a probability distribution over a set of observed variables is compatible with a given causal structure. In [arXiv:1609.00672], one of us introduced a hierarchy of necessary linear programming constraints which all the observed distributions compatible with the considered causal structure...

Contextuality is a particular quantum phenomenon that has no analogue in classical probability theory. Given two independent systems, a natural question is how to represent such a situation as a single test space. In other words, how separate contextuality scenarios combine into a joint scenario. Under the premise that the the allowed probabilistic...

Quantum theory is known to be nonlocal in the sense that separated parties can perform measurements on a shared quantum state to obtain correlated probability distributions, which cannot be achieved if the parties share only classical randomness. Here we find that the set of distributions compatible with sharing quantum states subject to some suffi...

This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Bell-type linear inequalities. In contrast to semidefinite programming approaches, ou...

We discuss the possibility of generating spin squeezed states by means of driven superradiance, analytically affirming and broadening the finding in [Phys. Rev. Lett. 110, 080502 (2013)]. In an earlier paper [Phys. Rev. Lett. 112, 140402 (2014)] the authors determined that spontaneous purely-dissipative Dicke model superradiance failed to generate...

An invited seminar to discuss research surrounding journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.140402. This presentation summarizes the primary finding of the published article, and also introduces our forthcoming work on entanglement generation via driven superradiance in slide 6.

Pending publication in Physics Review Letters. The published version is subject to strict word limits and is divided into a primary manuscript along and supplementary online materials. This is a unified manuscript which has not been formatted for the PRL, in which the supplementary material is included as appendices.

DRAFT - DO NOT DISTRIBUTE. This paper demonstrates a new mathematical formulation for the conventional Clebsch-Gordan coefficients using methods motivated by combinatoric arguments in the spirit of [Ann. Phys. 508 (1996)]. This simple and concise proof is predicated upon the treatment of all states involved in the angular momentum coupling as thoug...

An invited seminar to discuss the research surrounding pra.aps.org/abstract/PRA/v86/i1/e012123. This presentation contains some results which are not included in the aforementioned published article. Slide 10 provides proof that a Hermitian operator's largest eigenvalue corresponds the the root of its characteristic polynomial at which all the deri...

Poster summarizing the Certifying Separability paper.

DOI:https://doi.org/10.1103/PhysRevA.87.039907

Pre-arXiv presentation of results proving no entanglement generation in Dicke model superradiance.

A summary of work proving no entanglement in Dicke Model Superradiance. [Note - slides 19-23 are deprecated. A mathematical error was identified which prevents generalization from qubits to qudits.]

Bell’s inequalities are important to our understanding of quantum foundations and critical to several quantum technologies. A recent work [E. Wolfe and S. F. Yelin Phys. Rev. A 86 012123 (2012)] derived three parametrized families of two-particle, two-setting Bell inequalities. These inequalities are important as they theoretically explore a larger...

We study mixtures of permutation symmetric (Dicke) states, with a special focus on superradiance time evolution. For such systems we develop necessary separability criteria for general N-qubit systems based on the condition of Positive Partial Transpose. We also compose sufficient separability criteria for the specific cases of two and three qubits...

Given a family of states (mixtures of the Dicke states) we precompile a general N-qubit entanglement criterion. We use the developed criterion to study entanglement in superradiance evolution which is a special case of the Dicke states. [Note: recipient of "Best Presentation" award]

Phase behavior and structural properties of homogeneous and inhomogeneous core-softened (CS) fluid consisting of particles interacting via the potential, which combines the hard-core repulsion and double attractive well interaction, are investigated. The vapour-liquid coexistence curves and critical points for various interaction ranges of the pote...

In the course of certain lung diseases, the surface properties and the amount of fluids coating the airways changes and liquid bridges may form in the small airways blocking the flow of air, impairing gas exchange. During inhalation, these liquid bridges may rupture due to mechanical instability and emit a discrete sound event called pulmonary crac...