Novel methods to construct nonlocal sets of orthogonal product states in an arbitrary bipartite high-dimensional system

Xu, Ge; Jiang, Dong-Huan

doi:10.1007/s11128-021-03062-8

Cited by 50 publications

(9 citation statements)

References 42 publications

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“…The four squares ((1, 0), (1,9), (6, 0), (6,9) According to the parity of m and n, the structure of the set of states can be divided into four types (see figure 5). For more details on the sets of quantum states, the authors may see the reference [65]. Now let's start with the following example. }…”

Section: Theorem 3 ([65]mentioning

confidence: 99%

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Zheng

2022

New J. Phys.

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Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A \textbf{104}, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. Unexpectedly, the constructions of genuine hidden nonlocal sets without entanglement seems to be easier than that with entanglement. Therefore, this kind of nonlocality is rather different from the Bell nonlocality.

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Section: Theorem 3 ([65]mentioning

confidence: 99%

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Zheng

2022

New J. Phys.

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“…4). For more details on the sets of quantum states, the authors may see the reference [65]. Now let's start with the following example.…”

Section: })mentioning

confidence: 99%

“…Similarly, one finds that c m is the smallest integer which is larger than m/2. Similarly, one can construct a set with 2(m+n)−8 states which are inspired by Xu et al's results [65]…”

Section: })mentioning

confidence: 99%

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Li,

Zheng

2021

Preprint

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Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. As Bandyopadhyay and Halder have been pointed out, sets with genuine hidden nonloclity would lead to some applications on the data hiding.

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“…This is because every quantum state can be reproduced using classical systems of higher dimension. It is, however, possible to ensure the security by checking for nonlocally [61,62].…”

Section: Introductionmentioning

confidence: 99%

Semi-device-independent quantum key agreement protocol

Yang

Wang

et al. 2021

Quantum Inf Process

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In quantum key agreement (QKA), a shared key is established among two or more parties where each participant equally contributes its part to the shared key, and none of the participants can determine the shared key alone. Zhou et al. (Electron Lett 40(18):1149) gave the first QKA protocol based on quantum teleportation and since then quite a few variants and extensions have been proposed. However, none of the existing protocols are device-independent, i.e., all of them assume implicitly that the single-photon states or entangled states supplied to the participants are of certain form. In this work, we exploit the idea of the device-independent dimension witness for independent preparation and measurement devices proposed by Tavakoli (Phys Rev Lett 125:15050, 2020) and connect it with the QKA protocol (Chong and Hwang in Opt Commun 283:1192-1195 to present the concept of semi-device-independent QKA protocol for the first time.

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Novel methods to construct nonlocal sets of orthogonal product states in an arbitrary bipartite high-dimensional system

Cited by 50 publications

References 42 publications

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Semi-device-independent quantum key agreement protocol

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