We derive monogamy relations (tradeoffs) between strengths of violations of Bell's inequalities from the non-signaling condition. Our result applies to general Bell inequalities with an arbitrary large number of partners, outcomes and measurement settings. The method is simple, efficient and does not require linear programming. The results are used to derive optimal fidelity for asymmetric cloning in nonsignaling theories.
Characterizing trade-offs between simultaneous violations of multiple Bell inequalities in a large network of qubits is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for …
We show that monogamy of Bell's inequality violations, which is strictly weaker condition than no-signaling is enough to prove security of quantum key distribution. We derive our results for a whole class of monogamy constraints and generalize our results to any theory that communicating parties may have access to. Some of these theories do not respect no-signaling principle yet still allow for secure communication. This proves that no-signaling is only a sufficient condition for the possibility of secure communication, but not the necessary one. We also present some new qualitative results co…
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Indian Institute of Technology Jodhpur（印度理工学院焦浦分校）；Indian Institute of Science Education and Research Kolkata（印度科学教育与研究学院加尔各答）；TCG CREST
We present a method to derive Bell monogamy relations by connecting the complementarity principle with quantum non-locality. The resulting monogamy relations are stronger than those obtained from the no-signaling principle alone. In many cases, they yield tight quantum bounds on violation of single and multiple qubit correlation Bell inequalities. In contrast with the two-qubit case, a rich structure of possible violation patterns is shown to exist in the multipartite scenario.
Physical principles constraints the way nonlocal correlations can be distributed among distant parties in a Bell-type experiment. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed by a set of parties by the violation observed by a different set of parties. Here we show that the no-signaling principle yields a simple and tight monogamy relations for an important class of bipartite and multipartite Bell inequalities. We also link these trade-offs to the guessing probability--a key quantity in the device-independent informati…
In any theory satisfying the no-signaling principle correlations generated among spatially separated parties in a Bell-type experiment are subject to certain constraints known as monogamy relations. Recently, in the context of the black hole information loss problem it was suggested that these monogamy relations might be violated. This in turn implies that correlations arising in such a scenario must violate the no-signaling principle and hence can be used to send classical information between parties. Here, we study the amount of information that can be sent using such correlations. To this a…
We strengthen the set of Bell-type inequalities presented by Sun & Fei [Phys. Rev. A 74, 032335 (2006)] that give a classification for biseparable correlations and entanglement in tripartite quantum systems. We will furthermore consider the restriction to local orthogonal spin observables and show that this strengthens all previously known such tripartite inequalities. The quadratic inequalities we find indicate a type of monogamy of maximal biseparable three-particle quantum correlations, although the nonmaximal ones can be shared. This is contrasted to recently found monogamy inequalities fo…
Recently, Pawlowski [Phys. Rev. A 82, 032313 (2010)] claimed to have proven the security of a quantum key distribution by using only the monogamy of Bell's inequality violations. In the proof, however, he tacitly assumed that the eavesdropper's outcome is binary. The assumption cannot be justified because Eve's (eavesdropper's) power can only be limited by natural principle. We provide a counter-example for a step of the proof.
We consider three parties, A, B, and C, each performing one of two local measurements on a shared quantum state of arbitrary dimension. We characterize the trade-off between the nonlocality of the Bell correlations observed by AB and of those observed by AC. This generalizes Tsirelson's bound on the quantum value of the CHSH inequality, the latter being recovered when C is completely uncorrelated with AB. We also discuss the trade-off between Bell violations and local expectation values of observables that anticommute with the ones used in the Bell test.
The monogamy is a fundamental property of Bell nonlocality and contextuality. In this article, we studied the $n$-cycle noncontextual inequalities and generalized CHSH inequalities in detail and found the sufficient conditions for those inequalities to be hold. According to those conditions, we provide several kind of tradeoff relations: monogamy of generalized Bell inequalities in non-signaling framework, monogamy of cycle type noncontextual inequalities and monogamy between Bell inequality and noncontextual inequality in general no-disturbance framework. At last, some generic tradeoff relati…
Quantum correlations, in particular those, which enable to violate a Bell inequality \cite{BELL}, open a way to advantage in certain communication tasks. However, the main difficulty in harnessing quantumness is its fragility to, e.g, noise or loss of particles. We study the persistency of Bell correlations of GHZ based mixtures and Dicke states. For the former, we consider quantum communication complexity reduction (QCCR) scheme, and propose new Bell inequalities (BIs), which can be used in that scheme for higher persistency in the limit of large number of particles $N$. In case of Dicke stat…
In this reply I address the comment by W-Y. Hwang and O. Gittsovich on my paper [Phys. Rev. A {\bf 82}, 032313 (2010)]. The authors of the comment point out that I use implicit assumption that the alphabet of the eavesdropper is binary. They claim that such assumption is unrealistic. Here I show that even without this assumption the main result of my paper still holds.
A unified view on the phenomenon of monogamy exhibited by Bell inequalities and non-contextuality inequalities arising from the no-signaling and no-disturbance principles is presented using the graph-theoretic method introduced in \textit{Phys. Rev. Lett. 109, 050404 (2012)}. We propose a novel type of trade-off, namely Bell inequalities that do not exhibit monogamy features of their own can be activated to be monogamous by the addition of a local contextuality term. This is illustrated by means of the well-known $\mathcal{I}_{3322}$ inequality, and reveals a resource trade-off between biparti…
Two overlapping bipartite binary input Bell inequalities cannot be simultaneously violated as this would contradict the usual no-signalling principle. This property is known as monogamy of Bell inequality violations and generally Bell monogamy relations refer to trade-offs between simultaneous violations of multiple inequalities. It turns out that multipartite Bell inequalities admit weaker forms of monogamies that allow for violations of a few inequalities at once. Here we systematically study monogamy relations between correlation Bell inequalities both within quantum theory and under the so…
The phenomenon of monogamy of Bell inequality violations is interesting both from the fundamental perspective as well as in cryptographic applications such as the extraction of randomness and secret bits. In this article, we derive new and stronger monogamy relations for violations of Bell inequalities in general no-signaling theories. These relations are applicable to the class of binary output correlation inequalities known as XOR games, and to a restricted set of unique games. In many instances of interest, we show that the derived relation provides a significant strengthening over previous…
We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all no-signaling probability distributions. This maximization can be cast as a linear program. In a setting where three parties, A, B, and C, share an entangled quantum state of arbitrary dimension, we: (i) bound the trade-off between AB's and AC's violation of the CHSH inequality, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violati…
The monogamy relations satisfied by quantum correlation measures play important roles in quantum information processing. Generally they are given in summation form. In this note, we study monogamy relations in product form. We present product-form monogamy relations for Bell nonlocality for three-qubit and multi-qubit quantum systems. We then extend our studies to other quantum correlations such as concurrence.
Physical principles constrain the way nonlocal correlations can be distributed among distant parties. These constraints are usually expressed by monogamy relations that bound the amount of Bell inequality violation observed among a set of parties by the violation observed by a different set of parties. We prove here that much stronger monogamy relations are possible for nonsignalling correlations by showing how nonlocal correlations among a set of parties limit any form of correlations, not necessarily nonlocal, shared among other parties. In particular, we provide tight bounds between the vio…
A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlat…
Violation of a Bell inequality guarantees the existence of quantum correlations in a quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states. For a shared multipartite quantum state, we establish a connection between the monogamy of Bell inequality violation and genuine multi-site entanglement as well as monogamy-based multiparty quantum correlation measures. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family states w…
In this paper we demonstrate that the property of monogamy of Bell violations seen for no-signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the Gleason property of no-disturbance. We show how one can construct monogamies for contextual inequalities by using the graph-theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution. After establishing that all the subgraphs that are chordal graphs …
Nonclassical correlations have been found useful in many quantum information processing tasks, and various measures have been proposed to quantify these correlations. In this work, we mainly study one of nonclassical correlations, called measurement-induced nonlocality (MIN). First, we establish a close connection between this nonlocal effect and the Bell nonlocality for two-qubit states. Then, we derive a tight monogamy relation of MIN for any pure three-qubit state and provide an alternative way to obtain similar monogamy relations for other nonclassical correlation measures, including squar…
No-signaling theories, which can contain nonlocal correlations stronger than classical correlations but limited by the no-signaling condition, have deepened our understanding of the quantum theory. In principle, the nonlocality of these theories can be verified via Bell tests. In practice, however, inefficient detectors may make Bell tests unreliable, which is called the detection efficiency loophole. In this work, we show almost tight lower and upper bounds of the detector efficiency requirement for demonstrating the nonlocality of no-signaling theories, by designing a general class of Bell t…
Closed Timelike Curves (CTCs) are intriguing relativistic objects that allow for time travel to the past and can be used as computational resources. In Deutschian Closed Timelike Curves (D-CTCs), due to the monogamy of entanglement, non-local correlations between entangled states are destroyed. In contrast, for Postselected Closed Timelike Curves (P-CTCs), a second variant of CTCs, the non-local correlations are preserved. P-CTCs can be harnessed for the signaling of non-orthogonal states to the past without a disruption of causality. In this paper, we take up signaling to the past and show a …
Bell showed 50 years ago that quantum theory is nonlocal via his celebrated inequalities, turning the issue of quantum nonlocality from a matter of taste into a matter of test. Years later, Hardy proposed a test for nonlocality without inequality, which is a kind of "something-versus-nothing" argument. Hardy's test for $n$ particles induces an $n$-partite Bell's inequality with two dichotomic local measurements for each observer, which has been shown to be violated by all entangled pure states. Our first result is to show that the Bell-Hardy inequality arising form Hardy's nonlocality test is …
Monogamy inequalities for the way bipartite EPR steering can be distributed among N systems are derived. One set of inequalities is based on witnesses with two measurement settings, and may be used to demonstrate correlation of outcomes between two parties, that cannot be shared with more parties. It is shown that the monogamy for steering is directional. Two parties cannot independently demonstrate steering of a third system, using the same two-setting steering witness, but it is possible for one party to steer two independent systems. This result explains the monogamy of two-setting Bell ine…
The so called bipartite non-signaling boxes are systems whose statistics is constrained solely by the principle of no instantaneous signaling between distant locations. Such systems can exhibit much stronger correlations than those admitted by quantum mechanics. Inspired by quantum logic approach of Tylec and Kuś, J. Phys. A: Math. Theor. 48 (2015) 505303, we consider non-signaling boxes with three inputs per party, and extend the set of measurements with just a single {\it global} measurement - one that mimics quantum two-party Bell measurement. We then show that this seemingly mild extension…
We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the redu…
Assuming perfect detection efficiency, we present an (indeterministic) model for an EPR-Bohm experiment which reproduces the singlet correlations, without contradicting Bell's original locality condition. In this model we allow the probability distribution $ρ_λ$ of the state $λ$ at the source to depend parametrically on the orientation $ξ$ of one of the measuring devices: $ρ_λ(λ,ξ)$. In a Bell experiment, no-signaling between the source and each one of the devices would seem clearly sufficient to rule such an influence; however, not even schemes where the choice of observables takes place duri…
A Bell test separates quantum mechanics from a classical, local realist theory of physics. However, a Bell test cannot separate quantum physics from all classical theories. Classical devices supplemented with non-signaling correlations, e.g., the Popescu-Rohrlich "nonlocal box," can pass a Bell test with probability at least as high as any quantum devices can. After all, quantum entanglement does not allow for signaling faster than the speed of light, so in a sense is a weaker special case of non-signaling correlations. It could be that underneath quantum mechanics is a deeper non-signaling th…
Fundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term $\textbf{HNSQ}$ in the multi-party Bell scenario where some subsystems are locally quantum while the remaining subsystems are only constrained by the no-signaling principle. Speci…
This article identifies a series of properties common to all theories that do not allow for superluminal signaling and predict the violation of Bell inequalities. Intrinsic randomness, uncertainty due to the incompatibility of two observables, monogamy of correlations, impossibility of perfect cloning, privacy of correlations, bounds in the shareability of some states; all these phenomena are solely a consequence of the no-signaling principle and nonlocality. In particular, it is shown that for any distribution, the properties of (i) nonlocal, (ii) no arbitrarily shareable and (iii) positive s…
Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, precise characterization of the set of quantum correlations remained elusive. There are correlations compatible with the no-signaling principle and still beyond what can be achieved within quantum theory, which has motivated the search for physical principles and computational methods to decide the quantum or postquantum behavior of correlations. Here, we identify a feature of Bell correlations that …
There is currently much interest in the recycling of entangled systems, for use in quantum information protocols by sequential observers. In this work, we study the sequential generation of Bell nonlocality via recycling one or both components of two-qubit states. We first give a description of two-valued qubit measurements in terms of measurement bias, strength, and reversibility, and derive useful tradeoff relations between them. Then, we derive one-sided monogamy relations for unbiased observables, that strengthen the recent Conjecture in [S. Cheng {\it et al.}, Phys. Rev. A \textbf{104}, L…
We discuss a connection between Bell nonlocality and Bayesian games. This link offers interesting perspectives for Bayesian games, namely to allow the players to receive advice in the form of nonlocal correlations, for instance using entangled quantum particles or more general no-signaling boxes. The possibility of having such 'nonlocal advice' will lead to novel joint strategies, impossible to achieve in the classical setting. This implies that quantum resources, or more general no-signaling resources, offer a genuine advantage over classical ones. Moreover, some of these strategies can repre…
In this paper we focus on the underlying quantum structure of temporal correlations and show their peculiar nature which differentiate them from spatial quantum correlations. We show rigorously that a particular entangled history, which can be associated with a quantum propagator, is monogamous to conserve its consistency throughout time. Yet evolving systems violate monogamous Bell-like multi-time inequalities. This dichotomy, being a novel feature of temporal correlations, has its roots in the measurement process itself which is discussed by means of the bundles of entangled histories. We in…
Exploring Bell Nonlocality with Extremal Non-Signaling Boxes
Instituto Superior Técnico（里斯本高等技术学院）；Instituto de Telecomunicações（电信研究所）；Q*Bird BV（Q*Bird有限公司）；INL – International Iberian Nanotechnology Laboratory（伊比利亚纳米技术国际实验室）；Sorbonne Université, CNRS, LIP6（索邦大学，法国国家科学研究中心，LIP6实验室）；Zuse Institute Berlin（柏林祖斯研究所）；Universidad de Sevilla（塞维利亚大学）；Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla（塞维利亚大学卡洛斯一世理论与计算物理研究所）；Inria, ENS de Lyon, UCBL, LIP（法国国家信息与自动化研究所，里昂高等师范学院，里昂第一大学，LIP实验室）
In Bell scenario, any nonlocal correlation, shared between two spatially separated parties, can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the measurement settings. Recently, Bell scenario has been generalized into `semi-quantum' scenario where external quantum inputs are provided to the parties. We show that in `semi-quantum' scenario, entangled states produce correlations whose deterministic explanation is possible only if measurement independence is reduced. Thus in simulating quantum correlation `semi…
The no-signaling polytope associated to a Bell scenario with three parties, two inputs, and two outputs is found to have 53856 extremal points, belonging to 46 inequivalent classes. We provide a classification of these points according to various definitions of multipartite non-locality and briefly discuss other issues like the interconversion between extremal points seen as a resource and the relation of the extremal points to Bell-type inequalities.
We present a characterization of the set of non-signaling correlations in terms of a two dimensional representation that involves the maximal value of a Bell functional and the mutual information between the parties. In particular, we apply this representation to the bipartite Bell scenario with two measurements and two outcomes. In terms of these physically meaningful quantities and through numerical optimization methods and some analytical results, we investigate the frontier between the different subsets of the non-signaling correlations, focussing on the quantum and post-quantum ones. Fina…
Contextuality means non-existence of a joint distribution for random variables recorded under mutually incompatible conditions, subject to certain constraints imposed on how the identity of these variables may change across these conditions. In simple quantum systems contextuality is indicated by violations of Bell-type or Leggett-Garg-type inequalities. These inequalities, however, are predicated on the assumption of no-signaling, defined as invariance of the distributions of measurement results with respect to other (e.g., earlier in time) measurements' settings. Signaling makes the inequali…
Bell inequalities and nonlocality have been widely studied in one-dimensional quantum systems. As a kind of quantum correlation, it is expected that bipartite nonlocaity should be present in quantum systems, just as bipartite entanglement does. Surprisingly, for various models, two-qubit states do not violate Bell inequalities, i.e., they are local. Recently, it is realized that the results are related to the monogamy trade-off obeyed by bipartite Bell correlations, thus it is believed that for general translation invariant systems, two-qubit states should not violate the Bell inequality(Olive…
The nature of quantum correlations in strongly correlated systems has been a subject of intense research. In particular, it has been realized that entanglement and quantum discord are present at quantum phase transitions and able to characterize it. Surprisingly, it has been shown for a number of different systems that qubit pairwise states, even when highly entangled, do not violate Bell's inequalities, being in this sense local. Here we show that such a local character of quantum correlations is in fact general for translation invariant systems and has its origins in the monogamy trade-off o…
Recently, a physically realistic protocol amplifying the randomness of Santha-Vazirani sources producing cryptographically secure random bits was proposed; however for reasons of practical relevance, the crucial question remained open whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two no-signaling components and in a situation where the violation of a Bell inequality only guarantees that some outcomes of the device for specific inputs exhibit randomness? Here, we solve this question and…
Recently, a group of experiments tested local realism with random choices prepared by humans. These various tests were subject to additional assumptions, which lead to loopholes in the interpretations of almost all of the experiments. Among these assumptions are fair sampling, no signaling, and faithful reproduction of a Bell-type quantum model. We examined the data from 9 of 13 experiments and analyzed occurring anomalies in view of the above assumptions. We conclude that further tests of local realism need better setup calibration to avoid apparent signaling or necessity of the complicated u…
It is shown that the data of the Hensen et al. Bell test experiment exhibits anomalous postselection that can fully account for the apparent violation of the CHSH inequality. A simulation of a local realist model implementing similar postselection is presented. The model produces an apparent violation of CHSH indistinguishable from that of the experiment. The experimental data also appears to violate no-signaling, and it is shown how postselection can produce an artifactual violation of no-signaling. The Hensen et al. experiment does not succeed in rejecting classical locality and therefore do…
Random numbers are an important resource for applications such as numerical simulation and secure communication. However, it is difficult to certify whether a physical random number generator is truly unpredictable. Here, we exploit the phenomenon of quantum nonlocality in a loophole-free photonic Bell test experiment for the generation of randomness that cannot be predicted within any physical theory that allows one to make independent measurement choices and prohibits superluminal signaling. To certify and quantify the randomness, we describe a new protocol that performs well in an experimen…
