Cieśliński Paweł, Knips Lukas, Kowalczyk Mateusz, Laskowski Wiesław, Paterek Tomasz, Vértesi Tamás, Weinfurter Harald
Institute of Theoretical Physics and Astrophysics, Faculty of Mathematics, Physics and Informatics, University of Gdańsk, Gdańsk 80-308, Poland.
Max Planck Institute for Quantum Optics, Garching 85748, Germany.
Proc Natl Acad Sci U S A. 2024 Oct 29;121(44):e2404455121. doi: 10.1073/pnas.2404455121. Epub 2024 Oct 25.
Quantum mechanics imposes limits on the statistics of certain observables. Perhaps the most famous example is the uncertainty principle. Similar trade-offs also exist for the simultaneous violation of multiple Bell inequalities. In the simplest case of three observers, it has been shown that if two observers violate a Bell inequality, then none of them can violate any Bell inequality with the third observer, a property called monogamy of Bell violations. Forms of Bell monogamy have been linked to the no-signaling principle, and the inability of simultaneous violations of all inequalities is regarded as their fundamental property. Here, we show that the Bell monogamy does not hold universally and that in fact the only monogamous situation exists for only three observers. Consequently, the nature of quantum nonlocality is truly polygamous. We present a systematic methodology for identifying quantum states, measurements, and tight Bell inequalities that do not obey the monogamy principle for any number of more than three observers. The identified polygamous inequalities enable any subset of [Formula: see text] observers to reveal nonlocality, which is also shown experimentally by measuring Bell-type correlations of six-photon Dicke states. Our findings may be exploited for multiparty quantum key distribution as well as simultaneous self-testing of multiple nodes in quantum networks.
量子力学对某些可观测量的统计施加了限制。也许最著名的例子就是不确定性原理。对于同时违反多个贝尔不等式的情况，也存在类似的权衡。在三个观察者的最简单情形中，已经证明如果两个观察者违反一个贝尔不等式，那么他们中没有一个能与第三个观察者违反任何贝尔不等式，这种性质被称为贝尔违反的一夫一妻制。贝尔一夫一妻制的形式与无信号原理相关联，并且不能同时违反所有不等式被视为它们的基本性质。在此，我们表明贝尔一夫一妻制并不普遍成立，实际上唯一的一夫一妻制情形仅存在于三个观察者的情况。因此，量子非定域性的本质实际上是多配偶制的。我们提出了一种系统的方法，用于识别对于任意多于三个观察者的数量都不遵循一夫一妻制原则的量子态、测量以及紧密的贝尔不等式。所识别出的多配偶制不等式使任意[公式：见原文]个观察者的子集都能揭示非定域性，这也通过测量六光子迪克态的贝尔型关联在实验中得到了证明。我们的发现可用于多方量子密钥分发以及量子网络中多个节点的同时自测试。
