arXiv subjects

Ryszard Horodecki

Publications and source records attributed to Ryszard Horodecki.

At least 19 recordsLinked to original sources

arXiv2025

The operational no-signalling constraints and their implications

The study of quantum correlations within relativistic spacetimes, and the consequences of relativistic causality on information processing using such correlations, has gained much attention in recent years. In this paper, we establish a unified framework in the form of operational no-signalling constraints to study both nonlocal and temporal correlations within general relativistic spacetimes. We explore several intriguing consequences arising from our framework. Firstly, we show that the violation of the operational no-signalling constraints in Minkowski spacetime implies either a logical paradox or an operational infringement of Poincar\'{e} symmetry. We thereby examine and subvert recent claims in [Phys. Rev. Lett. 129, 110401 (2022)] on the possibility of witnessing operationally detectable causal loops in Minkowski spacetime. Secondly, we explore the possibility of jamming of nonlocal correlations, controverting a recent claim in [Nat. Comm. 16, 269 (2025)] that a physical mechanism for jamming would necessarily lead to superluminal signalling. Finally, we show that in black hole spacetimes certain nonlocal correlations under and across the event horizon can be jammed by any agent without spoiling the operational no-signalling constraints.

quant-ph↗

arXiv2024

Does Quantum Information Require Additional Structure?

We consider the status of quantum information in the quantum theory and based on the correspondence principle, we propose an interpretation of the wave function as a mathematical representation of quantum information. We consider Clauser's analysis of incompatibility formulations of quantum theory in laboratory space and configuration-space in the context of local realism. Then, we introduce the hypothesis of quantum space of directly unobserved relations, which precede quantum correlations, and are compatible with the Reichenbach common cause principle. The possible implications of the hypothesis are discussed in the context of the latest experimental and theoretical results on the dynamics of entanglement formation in helium atoms. Finally, we present the Chyli\'nski model as an example of quantum relational continuum space, which predicts potentially measurable effects for the bound states.

quant-ph↗

arXiv2024

Activation of metrologically useful genuine multipartite entanglement

We consider quantum metrology with several copies of bipartite and multipartite quantum states. We characterize the metrological usefulness by determining how much the state outperforms separable states. We identify a large class of entangled states that become maximally useful for metrology in the limit of large number of copies, even if the state is weakly entangled and not even more useful than separable states. This way we activate metrologically useful genuine multipartite entanglement. Remarkably, not only that the maximally achievable metrological usefulness is attained exponentially fast in the number of copies, but it can be achieved by the measurement of few simple correlation observables. We also make general statements about the usefulness of a single copy of pure entangled states. We surprisingly find that the multiqubit states presented in Hyllus et al. [Phys. Rev. A 82, 012337 (2010)], which are not useful, become useful if we embed the qubits locally in qutrits. We discuss the relation of our scheme to error correction, and its possible use for quantum metrology in a noisy environment.

quant-ph↗

arXiv2024

Comment on 'Quantum principle of relativity'

Dragan and Ekert in the paper (2020 \emph{New. J. Phys.} \textbf{22} 033038) presented 'quantum principle of relativity' (QPR) based on Galilean principle of relativity, which involves both superluminal $G_S$ and subluminal $G_s$ families of observers and argue that then they are considered on the same footing it 'implies the emergence of non-deterministic dynamics, together with complex probability amplitudes and multiple trajectories.'. Here we discuss QPR in the context of Heisenberg's classification of the fundamental physical theoretical models under the role universal constants of nature: Planck's constant $h$ and speed of light $c$. We point out that both the superluminal and subluminal branches are separable in the sense that there is no mathematical coherent formalism that connect both branches. This, in particular, implies that the QPR is incomplete.

quant-ph↗

arXiv2022

Non-perfect propagation of information to noisy environment with self-evolution

We study the non-perfect propagation of information to evolving low-dimensional environment that includes self-evolution as well as noisy initial states and analyze interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast structure formed during the interaction may exhibit non-monotonicity both in the speed of self-dynamics of the environment as well as its mixedness. The former effect is particularly strong, showing that -- considering part of the environment as a measurement apparatus -- an increase of the external magnetic field acting on the environment may turn the very vague measurement into close to ideal. The above effects suggest that quantum objectivity may appear after increasing the dynamics of the environment, although not with respect to the pointer basis, but some other one which we call generalized pointer or indicator basis. Furthermore, it seems also that when the objectivity is poor it may be improved, at least by some amount, by increasing thermal noise. We provide further evidence of that by analyzing the upper bounds on distance to the set of states representing perfect objectivity in the case of a higher number of qubits.

quant-ph↗

arXiv2022

The rank of contextuality

Quantum contextuality is one of the most recognized resources in quantum communication and computing scenarios. We provide a new quantifier of this resource, the rank of contextuality (RC). We define RC as the minimum number of non-contextual behaviors that are needed to simulate a contextual behavior. We show that the logarithm of RC is a natural contextuality measure satisfying several properties considered in the spirit of the resource-theoretic approach. The properties include faithfulness, monotonicity, and additivity under tensor product. We also give examples of how to construct contextual behaviors with an arbitrary value of RC exhibiting a natural connection between this quantifier and the arboricity of an underlying hypergraph. We also discuss exemplary areas of research in which the new measure appears as a natural quantifier.

quant-ph↗

arXiv2021

Quantum information

This article reviews the extraordinary features of quantum information predicted by the quantum formalism, which, combined with the development of modern quantum technologies, have opened new horizons in quantum physics that can potentially affect various areas of our live, leading to new technologies such as quantum cybersecurity, quantum communication, quantum metrology, and quantum computation.

quant-ph↗

arXiv2021

Activating hidden metrological usefulness

We consider bipartite entangled states that cannot outperform separable states in any linear interferometer. Then, we show that these states can still be more useful metrologically than separable states if several copies of the state are provided or an ancilla is added to the quantum system. We present a general method to find the local Hamiltonian for which a given quantum state performs the best compared to separable states. We obtain analytically the optimal Hamiltonian for some quantum states with a high symmetry. We show that all bipartite entangled pure states outperform separable states in metrology. Some potential applications of the results are also suggested.

quant-ph↗

arXiv2020

Generally covariant $N$-particle dynamics

A simultaneous description of the dynamics of multiple particles requires a configuration space approach with an external time parameter. This is in stark contrast with the relativistic paradigm, where time is but a coordinate chosen by an observer. Here we show, however, that the two attitudes toward modelling $N$-particle dynamics can be conciliated within a generally covariant framework. To this end we construct an '$N$-particle configuration spacetime' $\mathcal{M}_{\scriptscriptstyle (N)}$, starting from a globally hyperbolic spacetime $\mathcal{M}$ with a chosen smooth splitting into time and space components. The dynamics of multi-particle systems is modelled at the level of Borel probability measures over $\mathcal{M}_{\scriptscriptstyle (N)}$ with the help of the global time parameter. We prove that with any time-evolution of measures, which respects the $N$-particle causal structure of $\mathcal{M}_{\scriptscriptstyle (N)}$, one can associate a single measure on the Polish space of '$N$-particle wordlines'. The latter is a splitting-independent object, from which one can extract the evolution of measures for any other global observer on $\mathcal{M}$. An additional asset of the adopted measure-theoretic framework is the possibility to model the dynamics of indistinguishable entities, such as quantum particles. As an application we show that the multi-photon and multi-fermion Schrödinger equations, although explicitly dependent on the choice of an external time-parameter, are in fact fully compatible with the causal structure of the Minkowski spacetime.

math-ph↗

arXiv2020

Operational causality in spacetime

The no-signalling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of admissible correlations in composite systems. Here we unveil its complementary incarnation --- the 'dynamical no-signalling principle' ---, which forbids superluminal signalling via measurements on simple physical objects (e.g. particles) evolving in time. We show that it imposes strong constraints on admissible models of dynamics. The posited principle is universal --- it can be applied to any theory (classical, quantum or post-quantum) with well-defined rules of calculating detection statistics in spacetime. As an immediate application we show how one could exploit the Schrödinger equation to establish a fully operational superluminal protocol in the Minkowski spacetime. This example illustrates how the principle can be used to identify the limits of applicability of a given model of quantum or post-quantum dynamics.

quant-ph↗

arXiv2019

Operational foundations of complementarity and uncertainty relations

The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which they both exhibit deterministic statistics. However, the right-hand side of uncertainty relation is generally not operational as it depends on the quantum formalism. Also, while joint non-measurability of observables is an operational notion, the complementarity in Bohr sense (i.e. excess of information needed to describe the system) has not yet been expressed in purely operational terms. In this paper we propose a solution to these problems, by introducing an operational definition for complementarity, and further postulating uncertainty as a necessary price for complementarity in physical theories. In other words, we propose to put the (operational) complementarity as the right-hand side of uncertainty relation. Concretely, we first identify two different notions of uncertainty and complementarity for which the above principle holds in quantum mechanics. We also introduce postulates for the general measures of uncertainty and complementarity. In order to define quantifiers of complementarity we first turn to the simpler notion of independence that is defined solely in terms of statistics two observables. We also use our framework to define new complementarity indicators based on (i) performance of random access codes, (ii) geometrical properties of the body of observed statistics, and (iii) variation of information. We then show that they can be used to state uncertainty relations. Moreover, we show that non-signaling and uncertainty relation expressed by complementarity of type (ii) leads to the Tsirelson bound for CHSH inequality. Lastly, we show that a variant of Information Causality called Information Content Principle, can be interpreted as uncertainty relation in the above sense.

quant-ph↗

arXiv2019

Closed timelike curves and the second law of thermodynamics

One out of many emerging implications from solutions of Einstein's general relativity equations are closed timelike curves (CTCs), which are trajectories through spacetime that allow for time travel to the past without exceeding the speed of light. Two main quantum models of computation with the use of CTCs were introduced by Deutsch (D-CTC) and by Bennett and Schumacher (P-CTC). Unlike the classical theory in which CTCs lead to logical paradoxes, the quantum D-CTC model provides a solution that is logically consistent due to the self-consistency condition imposed on the evolving system, whereas the quantum P-CTC model chooses such solution through post-selection. Both models are non-equivalent and imply nonstandard phenomena in the field of quantum computation and quantum mechanics. In this work we study the implications of these two models on the second law of thermodynamics - the fundamental principle which states that in an isolated system the entropy never decreases. In particular, we construct CTC-based quantum circuits which lead to decrease of entropy.

gr-qc↗

arXiv2017

Zero knowledge convincing protocol on quantum bit is impossible

Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state $ϕ$, unknown to him. Alice knows $ϕ$ and she is supposed to convince Bob that she knows $ϕ$ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about $ϕ$ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state $ϕ$ with nonzero probability. This "no-go" result puts general constrains on information processing where information {\it about} quantum state is involved.

quant-ph↗

arXiv2017

No-signaling versus quantum constraints for spatio-temporal correlations caused by weak measurement

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty principle from two comprehensible assumptions: impossibility of instantaneous messaging at a distance (no-signaling), and violation of Bell inequalities (non-locality). The uncertainty is established for a pair of observables of one of two spatially separated systems that exhibit non-local correlations. To this end, we introduce a gentle form of measurement which acquires partial information about one of the observables. We then bound disturbance of the remaining observables by the amount of information gained from the gentle measurement, minus a correction depending on the degree of non-locality. The obtained quantitative expression resembles the quantum mechanical formulations, yet it is derived without the quantum formalism and complements the known qualitative effect of disturbance implied by non-locality and no-signaling.

quant-ph↗

arXiv2017

Do black holes create polyamory?

Of course not, but if one believes that information cannot be destroyed in a theory of quantum gravity, then we run into apparent contradictions with quantum theory when we consider evaporating black holes. Namely that the no-cloning theorem or the principle of entanglement monogamy is violated. Here, we show that neither violation need hold, since, in arguing that black holes lead to cloning or non-monogamy, one needs to assume a tensor product structure between two points in space-time that could instead be viewed as causally connected. In the latter case, one is violating the semi-classical causal structure of space, which is a strictly weaker implication than cloning or non-monogamy. We show that the lack of monogamy that can emerge in evaporating space times is one that is allowed in quantum mechanics, and is very naturally related to a lack of monogamy of correlations of outputs of measurements performed at subsequent instances of time of a single system. A particular example of this is the Horowitz-Maldacena proposal, and we argue that it needn't lead to cloning or violations of entanglement monogamy. For measurements on systems which appear to be leaving a black hole, we introduce the notion of the temporal product, and argue that it is just as natural a choice for measurements as the tensor product. For black holes, the tensor and temporal products have the same measurement statistics, but result in different type of non-monogamy of correlations, with the former being forbidden in quantum theory while the latter is allowed. In the case of the AMPS firewall experiment we find that the entanglement structure is modified, and one must have entanglement between the infalling Hawking partners and early time outgoing Hawking radiation which surprisingly tame violation of entanglement monogamy.

hep-th↗

arXiv2017

Measurement uncertainty from no-signaling and non-locality

quant-ph↗

arXiv2015

Nonsignaling quantum random access code boxes

A well known cryptographic primitive is so called random access code. Namely, Alice is to send to Bob one of two bits, so that Bob has the choice which bit he wants to learn about. However at any time Alice should not learn Bob's choice, and Bob should learn only the bit of his choice. The task is impossible to accomplish by means of either classical or quantum communication. On the other hand, a concept of correlations stronger than quantum ones, exhibited by so called Popescu- Rohrlich box, was introduced and widely studied. In particular, it is known that Popescu-Rohrlich box enables simulation of the random access code with the support of one bit of communication. Here, we propose a quantum analogue of this phenomenon. Namely, we define an analogue of a random access code, where instead of classical bits, one encodes qubits. We provide a quantum non-signaling box that if supported with two classical bits, allows to simulate a quantum version of random access code. We point out that two bits are necessary. We also show that a quantum random access code cannot be fully quantum: when Bob inputs superposition of two choices, the output will be in a mixed state rather than in a superposition of required states.

quant-ph↗

arXiv2014

Can communication power of separable correlations exceed that of entanglement resource?

The scenario of remote state preparation with shared correlated quantum state and one bit of forward communication [B. Dakic et al. Nature Physics 8, 666-670 (2012)] is considered. The transmission efficiency is examined by considering general encoding and decoding strategies. The importance of use of linear fidelity is recognized. It is shown that separable states cannot exceed the efficiency of entangled states in this protocol. It is proven however that such a surprising phenomena may naturally occur when the decoding agent has limited resources in the sense that either (i) has no information about the coordinates in the sender plane being in question or (ii) is forced to use bistochastic operations only which may be imposed by physically inconvenient local thermodynamical conditions.

quant-ph↗