Losses in the transmission channel, which increase with distance, pose a major obstacle to photonics demonstrations of quantum nonlocality and its applications. Recently, Chaturvedi, Viola, and Pawlowski (CVP) [arXiv:2211.14231] introduced a variation of standard Bell experiments with the goal of extending the range over which quantum nonlocality can be demonstrated. These experiments, which we call `routed Bell experiments', involve two distant parties, Alice and Bob, and allow Bob to route his quantum particle along two possible paths and measure it at two distinct locations – one near and another far from the source. The premise is that a high-quality Bell violation in the short-path should constrain the possible strategies underlying the experiment, thereby weakening the conditions required to detect nonlocal correlations in the long-path. Building on this idea, CVP showed that there are certain quantum correlations in routed Bell experiments such that the outcomes of the remote measurement device cannot be classically predetermined, even when its detection efficiency is arbitrarily low. In this paper, we show that the correlations considered by CVP, though they cannot be classically predetermined, do not require the transmission of quantum systems to the remote measurement device. This leads us to define and formalize the concept of `short-range' and `long-range' quantum correlations in routed Bell experiments. We show that these correlations can be characterized through standard semidefinite-programming hierarchies for non-commutative polynomial optimization. We then explore the conditions under which short-range quantum correlations can be ruled out and long-range quantum nonlocality can be certified in routed Bell experiments. We point out that there exist fundamental lower-bounds on the critical detection efficiency of the distant measurement device, implying that routed Bell experiments cannot demonstrate long-range quantum nonlocality at arbitrarily large distances. However, we do find that routed Bell experiments allow for reducing the detection efficiency threshold necessary to certify long-range quantum correlations. The improvements, though, are significantly smaller than those suggested by CVP's analysis.

中文翻译：

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通过路由贝尔测试验证远程量子相关性

传输通道中的损耗随着距离的增加而增加，这对量子非局域性的光子学演示及其应用构成了主要障碍。最近，Chaturvedi、Viola 和 Pawlowski (CVP) [arXiv:2211.14231] 引入了标准贝尔实验的变体，其目标是扩展量子非定域性的证明范围。这些实验，我们称之为“路由贝尔实验”，涉及两个遥远的一方，爱丽丝和鲍勃，并允许鲍勃沿着两条可能的路径路由他的量子粒子，并在两个不同的位置测量它——一个靠近源头，另一个远离源头。前提是短路径中的高质量贝尔违规应该限制实验中可能的策略，从而削弱长路径中检测非局部相关性所需的条件。基于这一想法，CVP 表明，路由贝尔实验中存在某些量子相关性，因此即使远程测量设备的检测效率任意低，其结果也无法通过经典方式预先确定。在本文中，我们表明，CVP 考虑的相关性虽然不能通过经典方式预先确定，但不需要将量子系统传输到远程测量设备。这导致我们在路由贝尔实验中定义并形式化了“短程”和“长程”量子相关性的概念。我们表明，这些相关性可以通过非交换多项式优化的标准半定规划层次结构来表征。然后，我们探讨了在路由贝尔实验中可以排除短程量子相关性并证明长程量子非定域性的条件。我们指出，远程测量装置的临界检测效率存在基本下限，这意味着路由贝尔实验无法证明任意长距离的长程量子非定域性。然而，我们确实发现路由贝尔实验可以降低验证长程量子相关性所需的检测效率阈值。不过，这些改进明显小于 CVP 分析建议的改进。