Tsirelson showed that $2\sqrt{2}$ is the maximum value that CHSH expression can take for quantum-correlations [B. S.Tsirelson, Lett. Math. Phys, 4 (1980) 93]. This bound simply follows from the algebra of observables. Recently by exploiting the physical structure of quantum mechanics like unitarity and linearity, Buhrman and Massar [H. Buhrman and S.Massar, Phys. Rev. A, 72 (2005) 052103] have established that violation of Tsirelson's bound in quantum mechanics will imply signalling. We prove the same with the help of realistic joint measurement in quantum mechanics and a Bell's inequality which has been derived under the assumption of existence of joint measurement and no signalling condition.
Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound from the axioms of nonlocality, relativistic causality and the existence of a classical limit. This derivation of Tsirelson's bound does not assume quantum mechanics yet suggests how Hilbert space is implicit in quantum correlations.
In order to analyze an information theoretical derivation of Tsirelson's bound based on information causality, we introduce a generalized mutual information (GMI), defined as the optimal coding rate of a channel with classical inputs and general probabilistic outputs. In the case where the outputs are quantum, the GMI coincides with the quantum mutual information. In general, the GMI does not necessarily satisfy the chain rule. We prove that Tsirelson's bound can be derived by imposing the chain rule on the GMI. We formulate a principle, which we call the no-supersignalling condition, which st…
The principle of `information causality' can be used to derive an upper bound---known as the `Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. To date, however, it has not been sufficiently motivated to play such a foundational role. The motivations that have so far been given are, as I argue, either unsatisfactorily vague or appeal to little if anything more than intuition. Thus in this paper I consider whether some way might be found to successfully motivate the principle. And I propose that a compelling…
Tsirelson's bound from a Generalised Data Processing Inequality
量子关联的强度从上到下受Tsirelson界的限制。我们建立了一个连接，这两个系统之间的相关性不能增加本地操作下，一个属性被称为数据处理不等式。更具体地说，我们考虑任意凸概率理论。这些可以配备一个熵的措施，自然推广冯诺伊曼熵，最近在[短和韦纳，巴纳姆等人]。我们证明，如果数据处理不等式持有关于这个广义熵测度，那么基本理论必然尊重Tsirelson的界限。此外，我们将这一说法推广到满足某些最小要求的任何熵测度。我们的结果的一个后果是，并不是所有的熵关系用于通过信息因果关系导出Tsirelson的约束[Pawlowski et al.]是必要的。
The term Bell's theorem refers to a set of closely related results which imply that quantum mechanics is incompatible with local hidden variable theories. Bell's inequality is the statement that if measurements are performed independently on two space-like separated particles of an entangled pair, the assumption that outcomes depend on hidden variables implies an upper bound on the correlations between the outcomes. Quantum mechanics predicts correlations which violate this upper bound. The CHSH inequality is a specific Bell inequality in which classical correlation (i.e. if local hidden varia…
Information causality was proposed as a physical principle to put upper bound on the accessible information gain in a physical bi-partite communication scheme. Intuitively, the information gain cannot be larger than the amount of classical communication to avoid violation of causality. Moreover, it was shown that this bound is consistent with the Tsirelson bound for the binary quantum systems. In this paper, we test the information causality for the more general (non-binary) quantum communication schemes. In order to apply the semi-definite programming method to find the maximal information ga…
Two physical principles, Macroscopic Locality (ML) and Information Causality (IC), so far, have been most successful in distinguishing quantum correlations from post-quantum correlations. However, there are also some post-quantum probability distributions which cannot be distinguished with the help of these principles. Thus, it is interesting to see whether consideration of these two principles, separately, along with some additional physically plausible constraints, can explain some interesting quantum features which are otherwise hard to reproduce. In this paper we show that, in a Bell-CHSH …
Information Causality is a physical principle which states that the amount of randomly accessible data over a classical communication channel cannot exceed its capacity, even if the sender and the receiver have access to a source of nonlocal correlations. This principle can be used to bound the nonlocality of quantum mechanics without resorting to its full formalism, with a notable example of reproducing the Tsirelson's bound of the Clauser-Horne-Shimony-Holt inequality. Despite being promising, the latter result found little generalization to other Bell inequalities because of the limitations…
In 1964, John Bell proved that quantum mechanics is "unreasonable" (to use Einstein's term): there are nonlocal bipartite quantum correlations. But they are not the most nonlocal bipartite correlations consistent with relativistic causality ("no superluminal signalling"): also maximally nonlocal "superquantum" (or "PR-box") correlations are consistent with relativistic causality. I show that---unlike quantum correlations---these correlations do not have a classical limit consistent with relativistic causality. The generalization of this result to all stronger-than-quantum nonlocal correlations…
One of Yakir Aharonov's endlessly captivating physics ideas is the conjecture that two axioms, namely relativistic causality ("no superluminal signalling") and nonlocality, so nearly contradict each other that a unique theory - quantum mechanics - reconciles them. But superquantum (or "PR-box") correlations imply that quantum mechanics is not the most nonlocal theory (in the sense of nonlocal correlations) consistent with relativistic causality. Let us consider supplementing these two axioms with a minimal third axiom: there exists a classical limit in which macroscopic observables commute. Th…
Information causality states that the information obtainable by a receiver cannot be greater than the communication bits from a sender, even if they utilize no-signaling resources. This physical principle successfully explains some boundaries between quantum and post-quantum nonlocal correlations, where the obtainable information reaches the maximum limit. We show that no-signaling resources of pure partially entangled states produce randomness (or noise) in the communication bits, and achievement of the maximum limit is impossible, i.e., the information causality principle is insufficient for…
A physical explanation for quantum bounds to nonlocality (Tsirelson's bound) is a fundamental problem that remains open, and one approach to explaining its origins is the so-called Exclusivity principle, relying on probabilistic assumptions shaping general probabilistic theories through sharp measurements and compatible (non-local) measurements. Information indistinguishability, presented here as indistinguishability of qubits and more general bits, may serve as an answer to the nonlocality conundrum, ultimately placing it as the origin to quantum limits. We connect indistinguishability to the…
The Suppes-Zanotti inequalities involving the joint expectations of just three binary quantum observables are (re-)derived by the hull computation of the respective correlation polytope. A min-max calculation reveals its maximal quantum violations correspond to a generalized Tsirelson bound. Notions of "contextuality" motivated by such violations are critically reviewed.
Formulas for calculating the joint probability of outcomes of measurements performed on mutually non-interacting component systems of a combined system prepared in an entangled state are presented. The formulas are based on non-relativistic quantum mechanics. An interpretation of the joint probability which conforms to the principle of local causality is proposed. The joint probability of outcomes of spin measurements performed on the well-known system of two spatially separated spin-1/2 particles prepared initially in the singlet state is used to illustrate the proposed interpretation of theo…
We propose the gentle measurement principle (GMP) as one of the principles at the foundation of quantum mechanics. It asserts that if a set of states can be distinguished with high probability, they can be distinguished by a measurement that leaves the states almost invariant, including correlation with a reference system. While GMP is satisfied in both classical and quantum theories, we show, within the framework of general probabilistic theories, that it imposes strong restrictions on the law of physics. First, the measurement uncertainty of a pair of observables cannot be significantly larg…
By representing an event as the joint state of a detector-timer couple that interact with a system, we recover the familiar tensor product structure, used to describe spatially separated systems, in the context of timelike events. Furthermore, with this approach, we extend the superposition principle to the moment of occurrence of events. We then outline quantum signatures of causality that manifest through coherence in the detector state and correlation functions of time operators. Finally, we expand the scope of quantum information theoretic measures of state discrimination and information c…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including but not reducible to what other measurements are made "together" with the given one. We propose in this paper that the quantum observables generating these random variables be labeled contextually as well, making the sets of the observables in different contexts disjoint. A quantum observable is defined as a pair consisting of the observable's label and a sel…
Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance & Continuity, at the foundation of those axiomatic reconstructions maps to "no preferred reference frame" (NPRF, aka "the relativity principle") as it pertains to the invariant measurement of Planck's constant h for Stern-Gerlach (SG) spin measure…
Characterising quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It has been shown that when considered with respect to so-called locally quantum observables, bipartite non-signalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum st…
Correlations of spins in a system of entangled particles are inconsistent with Kolmogorov's probability theory (KPT), provided the system is assumed to be non-contextual. In the Alice-Bob EPR paradigm, non-contextuality means that the identity of Alice's spin (i.e., the probability space on which it is defined as a random variable) is determined only by the axis \alphai chosen by Alice, irrespective of Bob's axis \betaj (and vice versa). Here, we study contextual KPT models, with two properties: (1) Alice's and Bob's spins are identified as Aij and Bij, even though their distributions are dete…
The uncertainty principle bounds the uncertainties about incompatible measurements, clearly setting quantum theory apart from the classical world. Its mathematical formulation via uncertainty relations, plays an irreplaceable role in quantum technologies. However, neither the uncertainty principle nor uncertainty relations can fully describe the complementarity between quantum measurements. As an attempt to advance the efforts of complementarity in quantum theories, we formally propose a complementary information principle, significantly extending the one introduced by Heisenberg. First, we bu…
