Recycling nonlocality in a quantum network

Mao, Ya-Li; Li, Zheng-Da; Steffinlongo, Anna; Guo, Bixiang; Liu, Biyao; Xu, Shufeng; Gisin, Nicolas; Tavakoli, Armin; Fan, Jingyun

doi:10.48550/arxiv.2202.04840

Cited by 4 publications

(7 citation statements)

References 63 publications

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“…In particular, the maximum number reduces to two when the shared state is close to maximally entangled states. After completion of our work, we notice that when both the observers share (noisy) maximally entangled states and want to employ network nonlocality by performing unsharp measurements in star and chain networks, a maximum of two rounds of detection for network nonlocal correlations is reported [43] (cf. also [42]).…”

Section: Discussionmentioning

confidence: 99%

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Limits of network nonlocality probed by time-like separated observers

Halder¹,

Banerjee²,

Mal³

et al. 2022

Preprint

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In an entanglement swapping scenario, if two sources sharing entangled states between three parties are independent, local correlations lead to a different kind of inequalities than the standard Bell inequalities, known as network local models. A highly demanding task is to find out a way to involve many players nontrivially in a quantum network since measurements, in general, disturb the system. To this end, we consider here a novel way of sharing network nonlocality when two observers initially share close to a maximally entangled state. We report that by employing unsharp measurements performed by one of the observers, six pairs can sequentially demonstrate the violation of bilocal correlations while a maximum of two pairs of observers can exhibit bi-nonlocality when both the observers perform unsharp measurements. We also find the critical noise involved in unsharp measurements in each round to illustrate the bi-nonlocality for a fixed shared entangled state as a resource. We also establish a connection between entanglement content of the shared state, quantified via von-Neumann entropy of the local density matrix for pure states and entanglement of formation for Werner states, and the maximum number of rounds showing violation of bilocal correlations. By reducing entanglement content in the elements of the joint measurement by the third party, we observe that the maximum number reduces to two sequential sharing of bi-nonlocality even for the maximally entangled state when the settings at each side are taken to be three and fixed.

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Section: Discussionmentioning

confidence: 99%

“…In the present work, we go beyond this picture (cf. [42,43]). In particular, we consider two independent sources which produce two noisy nonmaximally entangled states.…”

Section: Introductionmentioning

confidence: 99%

Limits of network nonlocality probed by time-like separated observers

Halder¹,

Banerjee²,

Mal³

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Optimal trade-off between quantum bound of elegant Bell inequality of Bob 1 , Bob 2 and Bob 3 are given by equation (66) and plotted in figure 4. The brown cube represents the preparation non-contextual bound showing no trade-off.…”

Section: Certification Of Multiple Unsharpness Parametersmentioning

confidence: 99%

“…Specifically, in our self-testing protocol, two sequential sub-optimal quantum violations of a Bell inequality form an optimal pair powering the DI certifications of the state, the local observables, and the unsharpness parameter of one of the two parties. We also note here that all the previous works that demonstrated the sharing of various quantum correlations [16,17,56,57,[60][61][62][63][64][65][66][67], the dimension of the system was assumed. In contrast, throughout this work, we impose no bound on the dimension of the Hilbert space, and we consider that the measurement devices are black boxes.…”

Section: Introductionmentioning

confidence: 99%

Device-independent self-testing of unsharp measurements

Roy

Pan

2023

New J. Phys.

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Semi-device-independent certification of an unsharp instrument has recently been demonstrated [New J. Phys. 21, 083034 (2019)] based on the sequential sharing of quantum advantages in a prepare-measure communication game by assuming the system to be qubit. In this work, we provide device-independent (DI) self-testing of the unsharp instrument through the quantum violation of two Bell inequalities where the devices are uncharacterized and the dimension of the system remains unspecified. We introduce an elegant sum-of-squares approach to derive the dimension-independent optimal quantum violation of Bell inequalities which plays a crucial role. Note that the standard Bell test cannot self-test the post-measurement states and consequently cannot self-test unsharp instruments. The sequential Bell test possesses the potential to self-test an unsharp instrument. We demonstrate that there exists a trade-off between the maximum sequential quantum violations of the Clauser-Horne-Shimony-Halt inequality, and they form an optimal pair that enables the DI self-testing of the entangled state, the observables, and the unsharpness parameter. Further, we extend our study to the case of elegant Bell inequality, and we argue that it has two classical bounds - the local bound and the non-trivial preparation non-contextual bound, lower than the local bound. Based on the sharing of preparation contextuality by three independent sequential observers, we demonstrate the DI self-testing of two unsharpness parameters. Since an experimental scenario involves losses and imperfection, we demonstrate the robustness of our certification to noise.

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“…Very recently, Cheng et al [37,38] showed that at most one pair of observers can share non-locality while considering the sharing for both parties. In recent years, a flurry of works have been reported to examine the number of independent sequential observers sharing different quantum correlations, viz., entanglement [39], steering [40][41][42], non-locality [35,36,[43][44][45][46][47] and preparation contextuality [32,48].…”

Section: Introductionmentioning

confidence: 99%

Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers

Kumari

Pan

2023

Phys. Rev. A

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Based on the quantum violation of bipartite Bell inequality, it has been demonstrated that the sharing of nonlocality can be demonstrated for at most two sequential observers at one end and at most one-pair of observers at both ends. In this work, we study the sharing of non-locality and preparation contextuality based on a bipartite Bell inequality, involving arbitrary n measurements by one party and 2 n−1 measurements by other party. Such a Bell inequality has two bounds, the local bound and the preparation non-contextual bound, which is smaller than the local bound. We show that while non-locality can be shared only by first pair of the sequential observers, the preparation contextuality can be shared by arbitrary pair of independent sequential observers at both ends.

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Recycling nonlocality in a quantum network

Cited by 4 publications

References 63 publications

Limits of network nonlocality probed by time-like separated observers

Limits of network nonlocality probed by time-like separated observers

Device-independent self-testing of unsharp measurements

Sharing preparation contextuality in a Bell experiment by an arbitrary pair of sequential observers

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