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arXiv 2311.04492quant-ph
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利用链式网络不等式的量子违反在网络中共享非定域性

Sharing nonlocality in a network using the quantum violation of chain network inequality

Rahul Kumar, A. K. Pan

备注：
arXiv admin note: text overlap with arXiv:2212.14325
发表信息：
Quantum Studies, 10, 353-372 (2023)
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AI总结：

本文研究星形网络中链式 n-局域不等式的量子违反，分析对称与非对称情形下连续观察者共享非定域性的数量界限，并给出任意输入数下的解析结果和最优量子违反。

摘要：

基于星形网络中针对任意 m 个输入的合适 n-局域不等式的量子违反，我们展示了网络中非定域性的共享。这种网络具有任意 n 个独立源、n 个边缘方和一个中央方。每一方接收任意 m 个输入。我们考虑网络中非定域性共享的两种不同类型：i）对称情形——当跨所有边缘方考虑非定域性共享时；ii）非对称情形——当仅跨一个边缘方考虑非定域性共享时。为简单起见，我们首先考虑具有三个输入 m=3 的双局域情形（n=2），并证明在对称情形下最多两个连续观察者可以共享非定域性，而在非对称情形下最多四个连续观察者可以共享非定域性。我们通过假设每一方接收三个输入，将研究扩展到 n-局域情形，并表明在对称情形下结果对任意 n 都保持不变；但在非对称情形下，对于足够大的 n 值，无限数量的连续观察者可以跨一条边共享非定域性。我们进一步将结果扩展到 n-局域情形中的任意 m 个输入。我们证明，对于 m≥4，在对称情形下，无论 n 的值如何，最多一个连续观察者可以共享非定域性。对于非对称情形，我们通过分析证明，存在 n(k)，使得任意 k 个连续观察者可以跨一条边共享非定域性。m-输入 n-局域不等式的最优量子违反是通过一种简洁的 SOS 方法导出的，无需指定量子系统的维度。

英文摘要：

Based on the quantum violation of suitable $n$-local inequality in a star network for arbitrary $m$ inputs, we demonstrate the sharing of nonlocality in the network. Such a network features an arbitrary $n$ number of independent sources, $n$ edge parties, and a central party. Each party receives arbitrary $m$ inputs. We consider two different types of sharing of nonlocality in the network. i) The symmetric case - when the sharing of nonlocality is considered across all edge parties. ii) The asymmetric case - when the sharing of nonlocality is considered across only one edge party. For simplicity, we first consider the bilocal scenario $(n=2)$ with three inputs $m=3$ and demonstrate that while in the symmetric case at most two sequential observers can share nonlocality, in the asymmetric case at most four sequential observers can share nonlocality. We extend the study to $n$-local scenario by assuming each party receives three inputs and show that in the symmetric case the result remains the same for any $n$, but in the asymmetrical case, an unbounded number of sequential observers can share nonlocality across one edge for a sufficiently large value of $n$. We further extend our result for arbitrary $m$ input in $n$-local scenario. We demonstrate that for $m\geq 4$, in the symmetric case at most one sequential observer can share nonlocality irrespective of the value of $n$. For the asymmetric case, we analytically show that there exists $n(k)$ for which an arbitrary $k$ number of sequential observers can share the nonlocality across one edge. The optimal quantum violation of $m$-input $n$-local inequality is derived through an elegant SOS approach without specifying the dimension of the quantum system.

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