Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

Junge, Marius; Palazuelos, Carlos; Pérez-Garcı́a, David; Villanueva, Ignacio; Wolf, Michael M.

doi:10.1007/s00220-010-1125-5

Cited by 57 publications

(90 citation statements)

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“…Roughly speaking, if violations of Bell inequalities mean that quantum mechanics is more powerful than classical mechanics, the amount of Bell violation quantifies how much more powerful it is (see [21][22][23] for some recent results in this direction). In order to define a measure of quantum nonlocality for a given state , let us denote Q the set of all quantum probabilities constructed with the state .…”

Section: 190401 (2012) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

“…LV measures exactly this. In fact, Proposition 3 in [22] allows us to write LV in the following alternative way, which emphasizes its connection to nonlocality:…”

Section: 190401 (2012) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

“…Ã ðMÞ ¼ supfjhM; Qij: Q 2 Qg and !ðMÞ ¼ supfjhM; Pij: P 2 Lg, and for every probability distribution P we denote hM; Pi ¼ X N;K x;y;a;b¼1 M a;b x;y pða; bjx; yÞ (see [21][22][23] for a complete study on this). Note that the existence of Bell violations can be stated by LVðMÞ > 1 for certain M's.…”

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Brunner¹,

Gisin²

2012

Physics

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In this Letter we show that quantum nonlocality can be superactivated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. In the second part of this work we study how large these violations can be. In particular, we show the existence of quantum states with very low Bell violation but such that five copies of them give very large violations. In fact, this gap can be made arbitrarily large by increasing the dimension of the states. DOI: 10.1103/PhysRevLett.109.190401 PACS numbers: 03.65.Ud, 03.65.Ta, 03.67.Mn The fact that by combining two quantum objects one can get something better than the sum of their individual uses seems to be a characteristic feature of quantum mechanics. In particular, in quantum information theory this effect has been extensively studied in quantum channel theory (see, for instance, [1][2][3]) and entanglement theory (see, for instance, [4,5]). Actually, some of these works show a much stronger behavior called superactivation. That is, one can get a quantum effect by combining two objects with no quantum effects. The aim of this work is to study this phenomenon in the context of quantum nonlocality.The study of quantum nonlocality dates back to the seminal work by Bell [6]. In this work the author took the apparently metaphysical dispute arising from the previous intuition of Einstein, Podolsky, and Rosen [7] and formulated it in terms of assumptions which naturally lead to a refutable prediction. Given two spatially separated quantum systems, controlled by Alice and Bob, respectively, and specified by a bipartite quantum state , Bell showed that certain probability distributions pða; bjx; yÞ obtained from an experiment in which Alice and Bob perform some measurements x and y in their corresponding systems with possible outputs a and b, respectively, cannot be explained by a local hidden variable model (LHVM). Specifically, Bell showed that the assumption of a LHVM implies some inequalities on the set of probability distributions pða; bjx; yÞ, since then called Bell inequalities, which are violated by certain quantum probability distributions produced with an entangled state.Though initially discovered in the context of foundations of quantum mechanics, violations of Bell inequalities, commonly known as quantum nonlocality, are nowadays a key point in a wide range of branches of quantum information science. In particular, nonlocal probability distributions provide the quantum advantage in the security of quantum cryptography protocols [8,9], in communication complexity protocols (see the recent review [10]), and in the generation of trusted random numbers [11].In order to pass from the probability distribution level to the quantum state level, we say that a bipartite quantum state is nonlocal if it can lead to certain quantum probability distributions pða; bjx; yÞ in an Alice-Bob scenario violating some Bell inequality. In the case where any probability distribution pða; bjx; yÞ produced with the state can be explained by a LHVM, we say ...

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Section: 190401 (2012) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

“…LV measures exactly this. In fact, Proposition 3 in [22] allows us to write LV in the following alternative way, which emphasizes its connection to nonlocality:…”

Section: 190401 (2012) P H Y S I C a L R E V I E W L E T T E R Smentioning

confidence: 99%

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Brunner¹,

Gisin²

2012

Physics

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“…This answered in the negative a question posed by Tsirelson about the possibility of a similar result to the one existing in the bipartite case. In the general bipartite case, several works have shown that one can also obtain unbounded Bell violations, and they have also studied how far these results are from being optimal [15,19]. On the other hand, strong techniques from computer science have also been used in this problem.…”

Section: Introductionmentioning

confidence: 99%

Large bipartite Bell violations with dichotomic measurements

Palazuelos

Yin

2015

Phys. Rev. A

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In this paper, we introduce a simple and natural bipartite Bell scenario by considering the correlations between two parties defined by general measurements in one party and dichotomic ones in the other. We show that unbounded Bell violations can be obtained in this context. Since such violations cannot occur when both parties use dichotomic measurements, so far our setting can be considered as the simplest one where this phenomenon can be observed. Our example is essentially optimal in terms of the outputs and the Hilbert space dimension.

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“…Much work has gone into determining bounds on quantum correlations [5][6][7][8][9][10][11][12], and investigating the difference between the classical and quantum regime (see e.g. [13,14]). …”

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confidence: 99%

Computability limits nonlocal correlations

Islam

Wehner

2012

Phys. Rev. A

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If the no-signalling principle was the only limit to the strength of non-local correlations, we would expect that any form of no-signalling correlation can indeed be realized. That is, there exists a state and measurements that remote parties can implement to obtain any such correlation. Here, we show that in any theory in which some functions cannot be computed, there must be further limits to non-local correlations than the no-signalling principle alone. We proceed to argue that even in a theory such as quantum mechanics in which non-local correlations are already weaker, the question of computability imposes such limits.Bell's seminal work [1] on non-local correlations, not only allowed us to distinguish classical from quantum mechanics, but also spurred a multitude of useful applications in quantum information theory (see e.g. [2,3]). As a result it is important to know which non-local correlations can indeed be physically realized.Let us now explain more carefully what is meant by non-local correlations. For simplicity, we thereby consider a bipartite system, Alice and Bob. Let X and Y denote a set of possible measurements for Alice and Bob respectively, and let A and B denote corresponding set of outcomes. Furthermore, letdenote the probability that Alice and Bob obtain outcomes a ∈ A and b ∈ B when making measurements x ∈ X and y ∈ Y respectively. When it comes to the study of non-local correlations, we are interested in the set of allowed values for Pr [a, b|x, y]. For example, the famous CHSH inequality [4] tells us that for any classical theory 1 4x,y∈{0,1} a∈{0,1}for any possible measurements labeled X = {0, 1} and Y = {0, 1}, and any state shared by Alice and Bob [31]. Quantumly, however, there exist a shared state and measurements such that the sum attains the value of 1/2 + 1/(2 √ 2) ≈ 0.853. This is the highest value possible in quantum mechanics [5]. It demonstrates that in a quantum world, non-local correlations can be strictly stronger than is allowed classically. Much work has gone into determining bounds on quantum correlations [5][6][7][8][9][10][11][12], and investigating the difference between the classical and quantum regime (see e

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Unbounded Violations of Bipartite Bell Inequalities via Operator Space Theory

Cited by 57 publications

References 57 publications

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Large bipartite Bell violations with dichotomic measurements

Computability limits nonlocal correlations

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