Understanding the structure of nonlocal correlations is important in many fields ranging from fundamental questions of physics to device-independent cryptography. We present a protocol that can convert extremal two-party--two-input nonlocal no-signaling boxes of any type into any other extremal two-party--two-input nonlocal no-signaling box perfectly. Our results are exact, and even though the number of required boxes cannot be determined in advance, their expected number is finite. Our protocol is adaptive and demonstrates for the first time the usefulness of using no-signaling boxes in different causal orders by the parties.
In this paper we study the correlations that arise when two separated parties perform measurements on systems they hold locally. We restrict ourselves to those correlations with which arbitrarily fast transmission of information is impossible. These correlations are called nonsignaling. We allow the measurements to be chosen from sets of an arbitrary size, but promise that each measurement has only two possible outcomes. We find the structure of this convex set of nonsignaling correlations by characterizing its extreme points. Taking an information-theoretic view, we prove that all of these ex…
Correlation boxes are hypothetical systems capable of producing the maximal algebraic violation of Bell inequalities, beyond the quantum bound and without superluminal signaling. The fact that these systems show stronger correlations than those presented by maximally entangled quantum states has been regarded as a demonstration that the former are more nonlocal than the latter. By employing an alternative, consistent measure of nonlocality, we show that this conclusion is not necessarily true. In addition, we find a class of correlation boxes that are less nonlocal than the quantum singlet wit…
The intriguing and powerful capability of nonlocality in communication field ignites the research of the nonlocality distillation. The first protocol presented in Ref[Phys. Rev. Lett. 102, 120401] shows that the nonlocality of bipartite binary-input and binary-output nonsignaling correlated boxes could be amplified by 'wiring' two copies of weaker-nonlocality boxes. Several optimized distillation protocols were presented later for bipartite binary-input and binary-output nonsignaling correlated boxes. In this paper, we focus on the bipartite binary-input and multi-nary-output nonsignaling corr…
The hypothetical nonlocal box (\textsf{NLB}) proposed by Popescu and Rohrlich allows two spatially separated parties, Alice and Bob, to exhibit stronger than quantum correlations. If the generated correlations are weak, they can sometimes be distilled into a stronger correlation by repeated applications of the \textsf{NLB}. Motivated by the limited distillability of \textsf{NLB}s, we initiate here a study of the distillation of correlations for nonlocal boxes that output quantum states rather than classical bits (\textsf{qNLB}s). We propose a new protocol for distillation and show that it asym…
We propose a class of nonlocal boxes named functional boxes which include a generalization of the Popescu-Rohrlich(PR) box as a special case. We show that every functional box corresponding to an additively inseparable function can make communication complexity trivial and thus seems unlikely to exist in nature. Then we relate general nonlocal boxes to these functional boxes, and derive several limits on them from the principle of information causality.
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）
Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishabil…
We show that standard nonlocal boxes, also known as Popescu-Rohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to the bipartite case. We then generalize this result further by showing that no finite set containing any finite-output-alphabet nonlocal boxes can be a universal set for nonlocality.
We show that standard nonlocal boxes, also known as Popescu-Rohrlich machines, are not sufficient to simulate any nonlocal correlations that do not allow signalling. This was known in the multipartite scenario, but we extend the result to the bipartite case. We then generalize this result further by showing that no finite set containing any finite-output-alphabet nonlocal boxes with uniform outputs can be a universal set for nonlocality.
We define a family of 'no signaling' bipartite boxes with arbitrary inputs and binary outputs, and with a range of marginal probabilities. The defining correlations are motivated by the Klyachko version of the Kochen-Specker theorem, so we call these boxes Kochen-Specker-Klyachko boxes or, briefly, KS-boxes. The marginals cover a variety of cases, from those that can be simulated classically to the superquantum correlations that saturate the Clauser-Horne-Shimony-Holt inequality, when the KS-box is a generalized PR-box (hence a vertex of the `no signaling' polytope). We show that for certain m…
We report the first experimental demonstration of distillation of quantum nonlocality, confirming the recent theoretical protocol [\textit{Phys. Rev. Lett. 102, 120401 (2009)}]. Quantum nonlocality is described by a correlation box with binary inputs and outputs, and the nonlocal boxes are realized through appropriate measurements on polarization entangled photon pairs. We demonstrate that nonlocality is amplified by connecting two nonlocal boxes into a composite one through local operations and four-photon coincidence measurements.
We show that there is a stronger form of bipartite quantum nonlocality in which systems that never interacted are as nonlocal as allowed by no-signaling. For this purpose, we first show that nonlocal boxes, theoretical objects that violate a bipartite Bell inequality as much as the no-signaling principle allows and which are physically impossible for most scenarios, are feasible if the two parties have 3 measurements with 4 outputs. Then we show that, in this case, entanglement swapping allows us to prepare mixtures of nonlocal boxes using systems that never interacted.
Reproducing with elementary resources the correlations that arise when a quantum system is measured (quantum state simulation), allows one to get insight on the operational and computational power of quantum correlations. We propose a family of models that can simulate von Neumann measurements in the x-y plane of the Bloch sphere on n-partite GHZ states using only bipartite nonlocal boxes. For the tripartite and fourpartite states, the models use only bipartite nonlocal boxes; they can be translated into classical communication schemes with finite average communication cost.
We carry out a thought experiment in an imaginary world. Our world is both local and realistic, yet it violates a Bell inequality more than does quantum theory. This serves to debunk the myth that equates local realism with local hidden variables in the simplest possible manner. Along the way, we reinterpret the celebrated 1935 argument of Einstein, Podolsky and Rosen, and come to the conclusion that they were right in their questioning the completeness of the Copenhagen version of quantum theory, provided one believes in a local-realistic universe. Throughout our journey, we strive to explain…
Einstein-Podolsky-Rosen steering is a form of quantum nonlocality which is weaker than Bell nonlocality, but stronger than entanglement. Here we present a method to check Einstein-Podolsky-Rosen steering in the scenario where the steering party performs two black-box measurements and the trusted party performs projective qubit measurements corresponding to two arbitrary mutually unbiased bases. This method is based on decomposing the measurement correlations in terms of extremal boxes of the steering scenario. In this context, we propose a measure of steerability called steering cost. We show …
Buhrman showed that an efficient communication protocol implies a reliable XOR game protocol. This idea rederives Linial and Shraibman's lower bounds of communication complexity, which was derived by using factorization norms, with worse constant factor in much more intuitive way. In this work, we improve and generalize Buhrman's idea, and obtain a class of lower bounds for classical communication complexity including an exact Linial and Shraibman's lower bound as a special case. In the proof, we explicitly construct a protocol for XOR game from a classical communication protocol by using a co…
Since its publication, Aharonov and Vaidman's three-box paradox has undergone three major advances: i). A non-counterfactual scheme by the same authors in 2003 with strong rather than weak measurements for verifying the particle's subtle presence in two boxes. ii) A realization of the latter by Okamoto and Takeuchi in 2016. iii) A dynamic version by Aharonov et al. in 2017, with disappearance and reappearance of the particle. We now combine these advances together. Using photonic quantum routers the particle acts like a quantum "shutter." It is initially split between Boxes A, B and C, the lat…
Supraquantum nonlocality refers to correlations that are more nonlocal than allowed by quantum theory but still physically conceivable in post-quantum theories, in the sense of respecting the basic no-faster-than-light communication principle. While supraquantum correlations are relatively well understood for finite-dimensional systems, little is known in the infinite-dimensional case. Here, we study supraquantum nonlocality for bipartite systems with two measurement settings and infinitely many outcomes per subsystem. We develop a formalism for generic no-signaling black-box measurement devic…
In the device-independent approach to quantum information theory, quantum systems are regarded as black boxes which, given an input (the measurement setting), return an output (the measurement result). These boxes are then treated regardless of their actual internal working. In this paper, we develop SWAP, a theoretical concept which, in combination with the tool of semi-definite methods for the characterization of quantum correlations, allows us to estimate physical properties of the black boxes from the observed measurement statistics. We find that the SWAP tool provides bounds orders of mag…
Nonlocality is arguably one of the most fundamental and counterintuitive aspects of quantum theory. Nonlocal correlations could, however, be even more nonlocal than quantum theory allows, while still complying with basic physical principles such as no-signaling. So why is quantum mechanics not as nonlocal as it could be? Are there other physical or information-theoretic principles which prohibit this? So far, the proposed answers to this question have been only partially successful, partly because they are lacking genuinely multipartite formulations. In Nat. Comm. 4, 2263 (2013) we introduced …
Brassard et al. [Phys. Rev. Lett. 96, 250401 (2006)] showed that shared nonlocal boxes with the CHSH probability greater than $\frac{3+\sqrt{6}}6$ yields trivial communication complexity. There still exists the gap with the maximum CHSH probability $\frac{2+\sqrt{2}}4$ achievable by quantum mechanics. It is an interesting open question to determine the exact threshold for the trivial communication complexity. Brassard et al.'s idea is based on the recursive bias amplification by the 3-input majority function. It was not obvious if other choice of function exhibits stronger bias amplification. …
A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a particle superposed over three boxes. Under appropriate pre- and postselections, and with tunneling enabled between two of the boxes, it is possible to derive not only one, but three predictions for three different times within the intermediate interval. These predictions are moreover contradictory. The particle (when looked for using a projective measurement) seems to disappear from the first box where it would have been previously found with certainty, appearing instead within the third box, to which no tunneling is…
It is shown that Popescu-Rohrlich nonlocal boxes (beating the Tsirelson bound for Bell inequality) do exist in the existing structures of both quantum and classical theory. In particular, we design an explicit example of measure-and-prepare nonlocal (but no-signaling) channel being the realization of nonlocal and no-signaling Popescu-Rohrlich box within the generalized probabilistic theory of processes. Further we present a post-selection-based spatially non-local implementation and show it does not require truly quantum resources, hence, improving the previously known results. Interpretation …
We have studied the possibility of post-quantum theories more nonlocal than the (standard) quantum theory using the modification of the quantum probability rule under the no-signaling condition. For this purpose we have considered the situation that two spacelike separate parties Alice and Bob share an entangled two qubit system. We have modified the quantum probability rule as small as possible such that the first local measurements are governed by the usual Born rule and the second measurement by the modified quantum probability rule. We have shown that only the maximally entangled states ca…
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 …
We propose a hidden variable analysis of collapse dynamics in which the state's reduction process may take a finite time $δt$. A full characterization of the model is given for the case of black boxes. By introducing nonlocal perfect correlations to a two black-boxes scenario, it is shown that in order to avoid faster than light communication, the reduction time associated to the system must be strictly null. Furthermore we prove that the result above holds even when there is a time window between the choice of both part's inputs. Our results represent a new evidence of the instantaneous natur…
In the well-studied (2,2,2) Bell experiment consisting of two parties, two measurement settings per party, and two possible outcomes per setting, it is known that if the experiment obeys no-signaling constraints, then the set of admissible experimental probability distributions is fully characterized as the convex hull of 24 distributions: 8 Popescu-Rohrlich (PR) boxes and 16 local deterministic distributions. Here, we refine this result to show that in the (2,2,2) case, any nonlocal nonsignaling distribution can always be uniquely expressed as a convex combination of exactly one PR box and (u…
