Measure-independent anomaly of nonlocality

Camalet, S.

doi:10.1103/physreva.96.052332

Cited by 16 publications

(14 citation statements)

References 46 publications

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“…such that {x, y} ∈ [−1, 1] and z ∈ [0, 1]. This strategy greatly reduces the dimensionality of the integration space; for now the violation condition (17) can be simply expressed as…”

Section: Comparison With Other Nonlocality Measuresmentioning

confidence: 99%

Nonanomalous measure of realism-based nonlocality

Gomes

Angelo

2018

Phys. Rev. A

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Based on a recently proposed model of physical reality and an underlying criterion of nonlocality for contexts [A. L. O. Bilobran and R. M. Angelo, Europhys. Lett. 112, 40005 (2015)], we introduce a quantifier of realismbased nonlocality for bipartite quantum states, a concept that is profoundly different from Bell nonlocality. We prove that this measure reduces to entanglement for pure states, thus being free of anomalies in arbitrary dimensions, and identify the class of states with null realism-based nonlocality. Then we show that such a notion of nonlocality can be positioned in a low level within the hierarchy of quantumness quantifiers, meaning that it can occur even for separable states. These results open a different perspective for nonlocality studies.

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“…such that {x, y} ∈ [−1, 1] and z ∈ [0, 1]. This strategy greatly reduces the dimensionality of the integration space; for now the violation condition (17) can be simply expressed as…”

Section: Comparison With Other Nonlocality Measuresmentioning

confidence: 99%

Nonanomalous measure of realism-based nonlocality

Gomes

Angelo

2018

Phys. Rev. A

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“…In this context the probability of violation under random measurements [28,29] has been proposed as a measure of nonlocality [30], and, contrary to these previous works, led to the conclusion that maximally entangled qutrits are maximally nonlocal. This indicates that the anomaly [31] in the nonlocality of entangled qudits may be an artefact of the previously employed measures (see however [32]). Recently, other promising quantifiers have been proposed, as, for example, a trace distance measure (within the context of a resource theory for nonlocality) [33], and a nonanomalous realism-based measure [34,35].…”

Section: Introductionmentioning

confidence: 99%

Survey on the Bell nonlocality of a pair of entangled qudits

et al. 2018

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The question of how Bell nonlocality behaves in bipartite systems of higher dimensions is addressed. By employing the probability of violation of local realism under random measurements as the figure of merit, we investigate the nonlocality of entangled qudits with dimensions ranging from d = 2 to d = 7. We proceed in two complementary directions. First, we study the specific Bell scenario defined by the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality. Second, we consider the nonlocality of the same states under a more general perspective, by directly addressing the space of joint probabilities (computing the frequencies of behaviours outside the local polytope). In both approaches we find that the nonlocality decreases as the dimension d grows, but in quite distinct ways. While the drop in the probability of violation is exponential in the CGLMP scenario, it presents, at most, a linear decay in the space of behaviours. Furthermore, in both cases the states that produce maximal numeric violations in the CGLMP inequality present low probabilities of violation in comparison with maximally entangled states, so, no anomaly is observed. Finally, the nonlocality of states with non-maximal Schmidt rank is investigated.

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“…Finally, we want to remark that the notion of activation of quantum nonlocality is known to hold in the context of 25,26]. Our result shows that activation of nonlocality also appears meaningfully in the context of quantum state discrimination by LOCC.…”

Section: Discussionmentioning

confidence: 61%

Genuine activation of nonlocality: From locally available to locally hidden information

Bandyopadhyay,

Halder

2021

Preprint

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Quantum nonlocality has different manifestations that, in general, are revealed by local measurements of the parts of a composite system. In this paper, we focus on the kind of nonlocality that arises from a set of orthogonal states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such a set is deemed nonlocal, for a joint measurement on the whole system is necessary for perfect discrimination of the states with certainty. On the other hand, a set of orthogonal states that can be perfectly distinguished by LOCC is believed to be devoid of nonlocal properties. In this paper, we study the properties of orthogonal sets that are locally distinguishable and without local redundancy. The latter implies that they become nonorthogonal on discarding one or more subsystems. We show that such a set may be locally converted, with certainty, into another orthogonal set of states that cannot be locally distinguished. Notably, the cardinality does not change in the process. We illustrate this with several examples. We also provide a partial characterization of those that do not have this property. Conceptually, our result can be viewed as activation of nonlocality in the scenario of local state discrimination. We also suggest an application, namely, local hiding of information, that allows us to locally hide the locally available information without losing any part. Once hidden, the information in its entirety can only be retrieved using entanglement.Quantum systems consisting of two or more subsystems may have nonlocal properties that, in general, are revealed by local measurements of the parts. Perhaps the most wellknown manifestation of quantum nonlocality, viz., Bell nonlocality [1-3] arises from entangled states [4] through their violation of Bell-type inequalities [5][6][7][8][9][10][11]. The latter implies that the predictions of quantum theory cannot be explained by any local theory. Bell nonlocality is of particular importance in quantum foundations [1], quantum information [1] and applications thereof. For example, Bell nonlocality tests are routinely used to certify device-independent quantum protocols [12][13][14][15][16].

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Measure-independent anomaly of nonlocality

Cited by 16 publications

References 46 publications

Nonanomalous measure of realism-based nonlocality

Nonanomalous measure of realism-based nonlocality

Survey on the Bell nonlocality of a pair of entangled qudits

Genuine activation of nonlocality: From locally available to locally hidden information

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