Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

Hsu, Li-Yi; Chen, Ching-Hsu

doi:10.1103/physrevresearch.3.023139

Cited by 7 publications

(10 citation statements)

References 34 publications

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“…In the upcoming study, we will explore Bell nonlocality with stabilizer states such as graph states [27,28] and codewords of stabilizer-based quantum error correction distributed in quantum networks [22]. The local observables therein can be made up of "cut-graft-mixing" stabilizing operators and logical operators [27].…”

Section: Discussionmentioning

confidence: 99%

“…Since long-distance quantum networks involving large-scale multi-users are the essential goals of upcoming quantum communication, it is fundamental to study their nonlocality strength in the network [11][12][13][14][15]. Specifically, the bilocality and K-locality correlations in the two-source and later the K-sources cases, respectively, have been extensively studied [16][17][18][19][20][21][22][23][24][25]. In most of the literature, however, the notions of bilocality and K-locality implicitly refer to the restricted distributions of local hidden variables.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Genuine Bell locality and its maximal violation in quantum networks

Hsu

2023

Phys. Scr.

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In K-locality networks, local hidden variables emitted from classical sources are distributed among limited observers. We explore genuine Bell locality in classical networks, where, regarding all local hidden variables as classical objects that can be perfectly cloned and spread throughout the networks, any observer can access all local hidden variables plus shared randomness. In the proposed linear and nonlinear Bell-type inequalities, there are more correlators to reveal genuine Bell locality than those in the K-locality inequalities, and their upper bounds can be specified using the probability normalization of the predetermined probability distribution. On the other hand, the no-cloning theorem limits the broadcast of quantum correlations in quantum networks. To explore genuine Bell nonlocality, the stabilizing operators play an important role in designing the segmented Bell operators and assigning the incompatible measurements for the spatially separated observers. We prove the maximal violations of the proposed Bell-type inequalities tailored for the given qubit distributions in quantum networks.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Genuine Bell locality and its maximal violation in quantum networks

Hsu

2023

Phys. Scr.

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“…Stabilisers have been employed to construct nonlocality and entanglement inequalities [24,29]. Nevertheless, homomorphism among stabiliser groups has not been hitherto studied, to the best of our knowledge, to derive a number of nonlocality inequalities given a seed nonlocality inequality.…”

Section: Relation With Previous Workmentioning

confidence: 99%

“…Thanks to its crucial applications, several approaches have been employed to derive nonlocality inequalities for numerous families of states such as graph states, cluster states, etc (see, for example [2,22,23], and references therein). Many nonlocality inequalities have been derived by employing stabiliser formalism, logical qubits [24] and by employing the action of abelian and non-abelian groups [25,26]. Additionally, a procedure for lifting Bell inequalities has also been proposed [27].…”

Section: Introductionmentioning

confidence: 99%

Interrelation of nonclassicality conditions through stabiliser group homomorphism

Asthana

2022

New J. Phys.

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In this paper, we show that coherence witness for a single qubit itself yields conditions for nonlocality and entanglement inequalities for multiqubit systems. It also yields a condition for quantum discord in two–qubit systems. It is shown by employing homomorphism among the stabiliser group of a single qubit and those of multi–qubit states. Interestingly, globally commuting homomorphic images of single qubit stabilisers do not allow for consistent assignments of outcomes of local observables. As an application, we show that CHSH inequality can be straightforwardly generalised to nonlocality inequalities for multiqubit GHZ states. It also reconfirms the fact that quantumness prevails even in the large N–limit, if coherence is sustained. The mapping provides a way to construct many nonlocality inequalities, given a seed inequality. This study gives us a motivation to gain a better control over multiple degrees of freedom and multi-party systems. It is because in multi-party systems, the same nonclassical feature, viz., coherence may appear in many avatars.

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“…With the development of quantum technology, quantum systems of medium scale have attracted much attention [30][31][32][33][34], such as quantum computation with noisy intermediate-scale quantum processors [35]. The researches on such quantum systems have spawned another kind of nonlocality that may be stronger than the Bell nonlocality -the quantum network nonlocality [36][37][38][39][40][41][42][43][44][45][46][47]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Sharing Quantum Nonlocality in Star Network Scenarios

Zhang¹,

Jing²,

Fei³

2022

Preprint

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The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality.

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Exploring Bell nonlocality of quantum networks with stabilizing and logical operators

Cited by 7 publications

References 34 publications

Genuine Bell locality and its maximal violation in quantum networks

Genuine Bell locality and its maximal violation in quantum networks

Interrelation of nonclassicality conditions through stabiliser group homomorphism

Sharing Quantum Nonlocality in Star Network Scenarios

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