Device-independent randomness based on a tight upper bound of the maximal quantum value of chained inequality

Xiao, Youwang; Li, Xinhui; Wang, Jing; Li, Ming; Fei, Shao-Ming

doi:10.1103/physreva.107.052415

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…Thus, our results can potentially serve as an effective criterion for the experimental detection of genuine multipartite non-locality and can be applied to various quantum information processing tasks. Finally, it would also be interesting to discover more insights in the multipartite scenarios by utilizing the upper bound in the context of sharing genuine non-locality, [28] the non-locality breaking property of channels [29] and device-independent secret sharing. [30] Appendix A: Proof of Lemma 2…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…[26], where the techniques arouse our interest in a deeper exploration of the N-partite generalized Svetlichny (GS) inequality. [19] In particular, the research for explicit analytical expressions for the maximal violation of the bipartite [27,28] and multipartite Bell inequalities for arbitrary quantum states is of great relevance, not only contributing to capture the deviation of quantum correlations from classical ones but also serving as a key component of secure cryptographic protocols. [26,29] In this work, we provide an analytical upper bound on the quantum expectation value of the generalized Svetlichny operators for an arbitrary N-qubit state for the two cases N even and N odd, respectively, with the intention of gaining a better understanding of GMNL by considering the generalized Svetlichny inequality.…”

Section: Introductionmentioning

confidence: 99%

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Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

Xiao,

Wang,

Zhao

et al. 2024

Adv Quantum Tech

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Genuine multipartite non‐locality is not only of fundamental interest but also serves as an important resource for quantum information theory. The ‐partite scenario and provide an analytical upper bound on the maximal expectation value of the generalized Svetlichny inequality achieved by an arbitrary ‐qubit system is considered. Furthermore, the constraints on quantum states for which the upper bound is tight are also presented and illustrated by noisy generalized Greenberger‐Horne‐Zeilinger states. Especially, the new techniques proposed to derive the upper bound allow more insights into the structure of the generalized Svetlichny operator and enable us to systematically investigate the relevant properties. As an operational approach, the variation of the correlation matrix defined makes it more convenient to search for suitable unit vectors that satisfy the tightness conditions. Finally, the results give feasible experimental implementations in detecting the genuine multipartite non‐locality and can potentially be applied to other quantum information processing tasks.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

Xiao,

Wang,

Zhao

et al. 2024

Adv Quantum Tech

Self Cite

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“…For example, for Bell nonlocality, there are methods such as Bell's inequality [14,15], Greenberg-Horn-Zeilinger paradox [16], and Hardy's paradox [17,18]. Similarly, inequality methods for EPR steering have been proposed, such as linear EPR steering inequality [19,20] and chained EPR steering inequality [21]. In addition, similar to the AVN argument for Bell nonlocality without inequalities, AVN proofs for EPR steering have been studied [22,23], among which, the EPR steering paradox [24,25] is also a very valuable method for studying EPR steering without inequalities, which reveals the steering nature of the quantum state through a logical contradiction between quantum mechanics and classical theory.…”

Section: Introductionmentioning

confidence: 99%

EPR steering paradox ‘2_Q = (2−δ)_C’

Liu,

Fan,

Zhou

et al. 2024

Phys. Scr.

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Einstein-Podolsky-Rosen (EPR) steering is a quantum nonlocality between entanglement and Bell’s nonlocality emphasizing the incompatibility of the local-hidden-state (LHS) model with quantum theory. It is well established that the EPR steering paradox is an essential method for determining steering, which reveals the nature of steering by logical contradiction. However, previous studies on the EPR steering paradox have only examined cases where the conditional states of the steered party are pure. In this work, we present the EPR steering paradox about the case when the conditional states of the steered party are mixed, which can be expressed as a paradoxical equality “2Q = (2 - δ)C” (0 < δ < 1) given by quantum (Q) and classical (C) theories. For any N-qubit state, in the two-setting steering protocol, the contradiction “2Q = (2 - δ)C” can be obtained if and only if a particular set of projective measurements of the steering party makes all the conditional states of the steered party pure, which also implies that the N-qubit state is steerable. Moreover, considering the conditional states of the steered party as mixed states, we are able to identify the full range of steerable states detectable through the EPR steering paradox method. This also means that, so far, one has found all the steerable states that can be recognized by the EPR steering paradox, which is signiﬁcant for some typical quantum schemes such as quantum teleportation and quantum key distribution.

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Bounding conditional entropy of bipartite states with Bell operators

Horodecki,

Mironowicz

2024

Phys. Rev. A

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Device-independent randomness based on a tight upper bound of the maximal quantum value of chained inequality

Cited by 3 publications

References 26 publications

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

EPR steering paradox ‘2_Q = (2−δ)_C’

Bounding conditional entropy of bipartite states with Bell operators

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Device-independent randomness based on a tight upper bound of the maximal quantum value of chained inequality

Cited by 3 publications

References 26 publications

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

Tight Upper Bound for the Maximal Expectation Value of the N$N$‐Partite Generalized Svetlichny Operator

EPR steering paradox ‘2 Q = (2−δ) C ’

Bounding conditional entropy of bipartite states with Bell operators

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EPR steering paradox ‘2_Q = (2−δ)_C’