Paweł Horodecki’s research while affiliated with University of Gdańsk and other places

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Publications (289)


Spacetime diagrams illustrating the protocol for superluminal signalling. The dashed lines show a preferred time-slicing. Alice and Bob travel along future-directed time-like curves (thin blue lines). Initially, they share a state |ψ⟩ generated at a source in their common past. (a) In the scenario considered in [15], Alice makes a local quantum measurement at t=t0 thus preparing some local state for Bob. Bob puts the later in his device, which operates until t=t1 (thick orange line). (b) In our scenario the evolution of the state |ψ⟩ is global, which is depicted by thin orange lines parallel to the time slices—see section 3.2 for the description. The events associated with Alice’s and Bob’s local operations are marked with black dots.
The time-evolution of the overlap between two global states initially separated by ε = 0.001 for different values of the concurrence C of the initial state |ψ(0)⟩. The parameters of the dynamics (24) are HA=HB=0 and g = 1.
The time-evolution of the overlap between two states under the dynamics (24) with a1=0.1, c = 0.413, d = 0.108, g = 1 and a2=b1=b2=0. The initial state |ψ(0)⟩=(|00⟩+|11⟩)/2 is maximally entangled state and ε = 0.001. The plots are shown on (a) the linear scale, and (b) the logarithmic scale.
The time-evolution of the concurrence for system (24) with parameters a1=0.2, c = 0.4, d = 0.5, g = 1 and a2=b1=b2=0. (a) The initial states are the Bell state (blue curve) and a state (29) with concurrence 1−ε, for ε = 0.001 (orange curve). (b) The case of separable initial states (30) with ε = 0.001.
An exemplary time-evolution of Bob’s reduced density matrix ρB(t).(a) The trajectory on the Bloch ball starts at the maximally mixed state (blue dot) and ends up in a partially mixed state (red dot). (b) The plot of the corresponding components of the Bloch vector.

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Superluminal signalling and chaos in nonlinear quantum dynamics
  • Article
  • Full-text available

May 2025

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28 Reads

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1 Citation

Marta Emilia Bielińska

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Michał Eckstein

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Paweł Horodecki

Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavours, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin proved a powerful no-go theorem, according to which nonlinear quantum dynamics would lead to superluminal signalling, violating Einstein’s causality. Here we analyse the theorem from the perspective of recent developments. First, we observe that it harmonises with the no-restriction hypothesis from General Probabilistic Theories. Second, we note that it requires a suitable synchronisation of Alice’s and Bob’s clocks and actions. Next, we argue that it does not automatically exclude the possibility of global nonlinear quantum dynamics on a tensor product Hilbert space. Consequently, we investigate a class of such dynamics inspired by discrete analogues of nonlinear Schrödinger equations. We show that, in general, they exhibit a chaotic character. In this context we inspect whether superluminal signalling can be avoided by relaxing the no-restriction hypothesis. We study three possible communication protocols involving either local measurements or modifications of a local Hamiltonian. We conclude that, in general, in all three cases, two spacelike separated parties can effectuate statistical superluminal information transfer. Nevertheless, we show an example of a nonlocal nonlinear quantum dynamics, which does not allow for it, provided that we relax the no-restriction hypothesis.

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FIG. 6. In this example, the graph G (2,3) consists of two maximum cliques C 1 and C 2 of size ω = 3.
Unbounded quantum advantage in communication with minimal input scaling

April 2025

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7 Reads

Physical Review Research

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Nitica Sakharwade

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[...]

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Paweł Horodecki

In communication complexity-like problems, previous studies have shown either an exponential quantum advantage or an unbounded quantum advantage with an exponentially large input set Θ ( 2 n ) bit with respect to classical communication Θ ( n ) bit. In the former, the quantum and classical separation grows exponentially in input while the latter's quantum communication resource is a constant. Remarkably, it was still open whether an unbounded quantum advantage exists while the inputs do not scale exponentially. Here we answer this question affirmatively using an input size of optimal order. Considering two variants as tasks: (1) distributed computation of relation and (2) , we study the one-way zero-error communication complexity of a relation induced by a distributed clique labeling problem for orthogonality graphs. While we prove no quantum advantage in the first task, we show an in relation reconstruction without public coins. Specifically, for a class of graphs with order m , the quantum complexity is Θ ( 1 ) while the classical complexity is Θ ( log 2 m ) . Remarkably, the input size is Θ ( log 2 m ) bit and the order of its scaling with respect to classical communication is . This is exponentially better compared to previous works. Additionally, we prove a lower bound (linear in the number of maximum cliques) on the amount of classical public coin necessary to overcome the separation in the scenario of restricted communication and connect this to the existence of orthogonal arrays. Finally, we highlight some applications of this task to semi-device-independent dimension witnessing as well as to the detection of mutually unbiased bases. Published by the American Physical Society 2025


Figure 2: Measurement of the entanglement marker D, where D < −1/3 indicates entanglement. Left panel: ATLAS particle-level D measurement compared with various MC models. Error bars represent all uncertainties included. The entanglement limit shown in the low m t ¯ t region is a conversion from its parton-level value of D = −1/3 to the corresponding value at particle-level [21]. Right panel: CMS parton-level D measurement either including (black filled point) or not including (black open point) contribution from toponium, compared to MC predictions with (solid line) or without (dashed line) the inclusion of toponium. Inner error bars represent the statistical uncertainty, while the outer error bars represent the total uncertainty for data [22].
Figure 3: Left panel: Comparison between two different approaches in the showering algorithm to the simulation of top-quark pair production as a function of the angular variable input to the entanglement witness D calculation [21]. Right Panel: Difference with respect to the SM prediction of several terms of the spin density matrix and entanglement witnesses (∆ + , ∆ − ) in top-quark pair production as a function of a coupling used to parametrize the presence of new physics in the SM vertices. The continuous line is obtained using only leading-order simulations, while the dashed line includes higher-order effects in QCD [52].
Quantum Information meets High-Energy Physics: Input to the update of the European Strategy for Particle Physics

March 2025

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63 Reads

Some of the most astonishing and prominent properties of Quantum Mechanics, such as entanglement and Bell nonlocality, have only been studied extensively in dedicated low-energy laboratory setups. The feasibility of these studies in the high-energy regime explored by particle colliders was only recently shown, and has gathered the attention of the scientific community. For the range of particles and fundamental interactions involved, particle colliders provide a novel environment where quantum information theory can be probed, with energies exceeding, by about 12 orders of magnitude, the laboratory setups typically used in the field. Furthermore, collider detectors have inherent advantages in performing certain quantum information measurements, and allow for the reconstruction the state of the system under consideration via quantum state tomography. Here, we elaborate on the potential, challenges, and goals of this innovative and rapidly evolving line of research, and discuss its expected impact on both quantum information theory and high-energy physics.


The task G (n,d,k) considers n spatially separated parties A1, A2, ⋯, An who only pre-share a multipartite system, each with local operational dimension d, prepared using PA1,A2,⋯,An and have access to some uncharacterized during device. Using these resources they generate outcomes a1, a2, ⋯, an∈{0,1,⋯,k−1} respectively. The joint probability of these outcomes is later used to detect qudit non-projective measurements using a set of target correlations or a payoff function.
The correlations in the set T2[2,2,3] that can be obtained using qubit non-projective measurement. Here x,y denotes the probability of each event where the outcomes are correlated and anti-correlated respectively. Correlations in the region R1 and R2 can be obtained using trine local measurements on the shared qubit state ρp (mixture of maximally entangled state |ψ−⟩ and maximally mixed state) and rotated trine local measurements on ρ~p (mixture of maximally entangled state |ψ+⟩ and maximally mixed state) respectively. The correlations in the region R4 cannot be obtained using any local quantum measurements on a two-qubit shared state. The realizability of the correlations in the region R3 with shared states of local dimension 2 is unknown.
The graph shows the correlations in the set T2[2,2,4] that can be obtained using qubit non-projective measurement. Here x,y denotes the probability of each event where the outcomes are correlated and anti-correlated respectively. Correlations in the region R1 and R2 can be obtained using SIC-POVM local measurements on the shared two-qubit state ρp (mixture of maximally entangled state |ψ−⟩ and maximally mixed state) and rotated SIC-POVM local measurements on ρ~p (mixture of maximally entangled state |ϕ+⟩ and maximally mixed state) respectively. The correlations in the region R4 cannot be obtained using any local quantum measurements on a two-qubit shared state. The realizability of the correlations in the region R3 with shared states of local dimension 2 is unknown.
The local measurement strategies for obtaining TPR: The black square denotes the local elementary effect space of the boxworld. Alice and Bob perform the measurements, each with three effects given by the vertices of the violet and blue triangles, respectively, on their subsystems of the bipartite state ωAB.
Randomness-free detection of non-projective measurements: qubits & beyond

March 2025

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29 Reads

Non-projective measurements play a crucial role in various information-processing protocols. In this work, we propose an operational task to identify measurements that are neither projective nor classical post-processing of data obtained from projective measurements. Our setup involves space-like separated parties with access to a shared state with bounded local dimensions. Specifically, in the case of qubits, we focus on a bipartite scenario with different sets of target correlations. While some of these correlations can be obtained through non-projective measurements on a shared two-qubit state, it is impossible to generate these correlations using projective simulable measurements on bipartite qubit states, or equivalently, by using one bit of shared randomness and local post-processing. For certain target correlations, we show that detecting qubit non-projective measurements is robust under arbitrary depolarizing noise, except in the limiting case. We extend this task for qutrits and demonstrate that some correlations achievable via local non-projective measurements cannot be reproduced by both parties performing the same qutrit projective simulable measurements on their pre-shared state. We provide numerical evidence for the robustness of this scheme under arbitrary depolarizing noise. For a more generic consideration (bipartite and tripartite scenario), we provide numerical evidence for a projective-simulable bound on the reward function for our task. We also show a violation of this bound by using qutrit positive operator valued measures. From a foundational perspective, we extend the notion of non-projective measurements to general probabilistic theories (GPTs) and use a randomness-free test to demonstrate that a class of GPTs, called square-bits or box-world are unphysical.


Three-Body Non-Locality in Particle Decays

February 2025

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5 Reads

The exploration of entanglement and Bell non-locality among multi-particle quantum systems offers a profound avenue for testing and understanding the limits of quantum mechanics and local real hidden variable theories. In this work, we examine non-local correlations among three massless spin-1/2 particles generated from the three-body decay of a massive particle, utilizing a framework based on general four-fermion interactions. By analyzing several inequalities, we address the detection of deviations from quantum mechanics as well as violations of two key hidden variable theories: fully local-real and bipartite local-real theories. Our approach encompasses the standard Mermin inequality and the tight 4×4×24 \times 4 \times 2 inequality introduced by Laskowski et al., providing a comprehensive framework for probing three-partite non-local correlations. Our findings provide deeper insights into the boundaries of classical and quantum theories in three-particle systems, advancing the understanding of non-locality in particle decays and its relevance to particle physics and quantum foundations.




Superluminal signalling and chaos in nonlinear quantum dynamics

December 2024

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16 Reads

Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin proved a powerful no-go theorem, according to which nonlinear quantum dynamics would lead to superluminal signalling, violating Einstein's causality. Here we analyse the theorem from the perspective of recent developments. First, we observe that it harmonises with the no-restriction hypothesis from General Probabilistic Theories. Second, we note that it requires a suitable synchronisation of Alice's and Bob's clocks and actions. Next, we argue that it does not automatically exclude the possibility of global nonlinear quantum dynamics on a tensor product Hilbert space. Consequently, we investigate a class of such dynamics inspired by discrete analogues of nonlinear Schr\"odinger equations. We show that, in general, they exhibit a chaotic character. In this context we inspect whether superluminal signalling can be avoided by relaxing the no-restriction hypothesis. We study three possible communication protocols involving either local measurements or modifications of a local Hamiltonian. We conclude that, in general, in all three cases, two spacelike separated parties can effectuate statistical superluminal information transfer. Nevertheless, we show an example of a nonlocal nonlinear quantum dynamics, which does not allow for it, provided that we relax the no-restriction hypothesis.


Prospects for quantum process tomography at high energies

December 2024

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2 Reads

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1 Citation

In quantum information theory, the evolution of an open quantum system -- a unitary evolution followed by a measurement -- is described by a quantum channel or, more generally, a quantum instrument. In this work, we formulate spin and flavour measurements in collider experiments as a quantum instrument. We demonstrate that the Choi matrix, which completely determines input-output transitions, can be both theoretically computed from a given model and experimentally reconstructed from a set of final state measurements (quantum state tomography) using varied input states. The reconstruction of the Choi matrix, known as quantum process tomography, offers a powerful new approach for probing potential extensions of the Standard Model within the quantum field theory framework and also provides a fundamental test of quantum mechanics itself. As an example, we outline a quantum process tomography approach applied to the e+ettˉe^+ e^- \to t \bar{t} process at a polarized lepton collider.


Randomness-free Detection of Non-projective Measurements: Qubits & beyond

November 2024

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4 Reads

Non-projective measurements are resourceful in several information-processing protocols. In this work, we propose an operational task involving space-like separated parties to detect measurements that are neither projective nor a classical post-processing of data obtained from a projective measurement. In the case of qubits, we consider a bipartite scenario and different sets of target correlations. While some correlations in each of these sets can be obtained by performing non-projective measurements on some shared two-qubit state it is impossible to simulate correlation in any of them using projective simulable measurements on bipartite qubit states or equivalently one bit of shared randomness. While considering certain sets of target correlations we show that the detection of qubit non-projective measurement is robust under arbitrary depolarising noise (except in the limiting case). For qutrits, while considering a similar task we show that some correlations obtained from local non-projective measurements are impossible to be obtained while performing the same qutrit projective simulable measurements by both parties. We provide numerical evidence of its robustness under arbitrary depolarising noise. For a more generic consideration (bipartite and tripartite scenario), we provide numerical evidence for a projective-simulable bound on the reward function for our task. We also show a violation of this bound by using qutrit POVMs. From a foundational perspective, we extend the notion of non-projective measurements to general probabilistic theories (GPTs) and use a randomness-free test to demonstrate that a class of GPTs, called square-bits or box-world are unphysical.


Citations (47)


... In 1989 Gisin [10,11] showed that nonlinear quantum dynamics would lead to superluminal signaling. This effect was investigated repeatedly [12][13][14], yielding both claims that no superluminal signaling implies linearity [15][16][17][18] and nonlinear modifications of quantum theories that do not feature superluminal signaling [19][20][21][22][23][24][25][26]. Certain nonlinear effects in quantum theory were also proposed to be experimentally tested [27,28] and some of the experiments were also carried out [29][30][31]. ...

Reference:

Ruling out nonlinear modifications of quantum theory with contextuality
Superluminal signalling and chaos in nonlinear quantum dynamics

... As a fundamentally distinct way of energy transfer between physical systems, nonreciprocity, stemming from the violation of the Lorentz reciprocity theorem, endows the system with the capacity to exhibit disparate responses for forward and backward energy transmission [18][19][20]. Beyond its functional applications in devices for unidirectional signal routing [21][22][23][24][25][26][27][28][29][30][31][32][33], nonreciprocity also provides an innovative means of manipulating captivating phenomena, including exceptional topology [34][35][36][37][38], phase transitions [39][40][41] and quantum correlations [42][43][44][45][46]. Recent studies have further broadened the exploration of nonreciprocity in manipulating energy transfer between quantum systems [47,48]. However, the investigation into the impact of nonreciprocity on the charging performance of quantum multi-battery models remains largely unexplored. ...

Superoptimal charging of quantum batteries via reservoir engineering: Arbitrary energy transfer unlocked
  • Citing Article
  • February 2025

Physical Review Applied

... Moving beyond the bipartite case, real-world scenarios often involve networks consisting of multiple parties [29][30][31][32] where entanglement distribution can be intricate. The strongest form of entanglement in a multipartite system is the genuine multipartite entanglement (GME) [33,34]. GME is a crucial resource in various quantum information tasks, including communication complexity [35,36], quantum thermodynamics [37][38][39], and quantum key distribution [40,41]. ...

Multipartite Entanglement

... Exploring the question of typical and average quantum correlations for such state ensembles is an interesting question in its own right, but it has also shown to be relevant in other areas of physics beyond quantum information, namely in the context of the black hole information paradox [44,45], quantum chaos [7,46,47] and many-body quantum systems [48,49]. In particular, a number of recent studies [4,6,7,10,46] have firmly established that the average entanglement entropy of energy eigenstates matches the one of Haar distributed random states at leading order (and even some subleading order in system size) for quantum-chaotic Hamiltonians. ...

Random Pure Gaussian States and Hawking Radiation

Physical Review Letters

... For instance, Ref. [107] studied the possibility of composing process matrices, Ref. [108] addressed the discrimination of process matrices and Ref. [23] proposed and implemented a scheme for process matrix tomography. The possibility of process matrices evolving in time was studied in Ref. [109]. Lastly, Refs. ...

Revisiting Dynamics of Quantum Causal Structures—When Can Causal Order Evolve?

... An alternative method for detecting entanglement is using entanglement witnesses (EWs), which are operators that identify entanglement by measuring their expectation values [19][20][21][22][23][24]. EWs offer a way to differentiate between entangled and nonentangled states without quantifying the degree of entanglement. ...

Sensitivity versus selectivity in entanglement detection via collective witnesses

Physical Review Research

... Nowadays, as material samples are brought to increasingly lower temperature and smaller sizes, we are experiencing a sort of nanoscale industrial revolution, where the challenge of energy storage takes on a quantum mechanical dimension, where centuries-old thermodynamical concepts are in need to be revisited in the face of non-classical resources such as quantum coherence and entanglement [3][4][5]. Indeed, the interplay between entanglement generation and work extraction from many-body quantum states has spurred a sustained research effort into quantum batteries [6][7][8][9][10][11][12][13][14]. ...

Nonreciprocal Quantum Batteries
  • Citing Article
  • May 2024

Physical Review Letters

... However, optimal solutions to the quantum brachistochrone problem do not always saturate the QSL bounds associated with the evolution of a single quantum state [28]. While a significant body of literature has focused on the QSL for the evolution of individual states, the exploration of QSLs governing the evolution of sets of quantum states remains in its early stages [29][30][31][32]. ...

Quantum speed limits for change of basis

... In particular, any property of a quantum state that is absent in a single copy, but that can be activated with many copies, could also be activated catalytically according to Lemma 1, as long τ A ′ B ′ in Eq. (7) also carries this property. For example, it has been shown that metrological advantage of certain entangled states can be activated in the many-copy regime [47]. From our results, it follows that catalytic activation of metrological advantage is possible. ...

Activation of metrologically useful genuine multipartite entanglement