多体场景中的局部友好型多面体研究
近日，澳大利亚格里菲斯大学的Marwan Haddara与Eric G. Cavalcanti合作并取得一项新进展。经过不懈努力，他们对多体场景中的局部友好型多面体进行研究。相关研究成果已于2025年1月9日在国际知名学术期刊《物理评论A》上发表。
在这项工作中，研究人员将局部友好性的研究扩展到多体场景——涉及任意但有限数量的超观测者、朋友、测量和结果——并全面描述了相应的局部友好性（LF）多面体、它们彼此之间的关系，以及与贝尔多面体、无信号多面体和量子关联集的关系。特别是，研究人员通过构造性证明，确定了所有局部友好性多面体与贝尔多面体重合的典型局部友好性场景，从而确定了所有可能出现“真正局部友好性不等式”的场景。
除此之外，研究人员还证明了，只要局部友好性多面体不同于贝尔多面体和无信号多面体，它就既不包含于也不包含量子关联集。除了更好地理解局部友好性所带来的约束这一基础性动机外，这项研究结果还可能在看似无关的器件无关信息处理领域找到应用，在该领域中，局部友好性多面体（被称为“部分确定性多面体”）也已被证明会出现。
据悉，近期，局部友好性（LF）不可行定理因其深刻的理论基础意义而引起了广泛关注。该不可行定理适用于将贝尔实验与维格纳的朋友类型设置相结合的场景，这些场景中包含有时空上分离的超观测者，他们被假设能够对局部观测者（也称为他们的“朋友”）执行量子操作。该定理表明，一组被称为“局部友好性”的假设——这组假设弱于证明贝尔定理所需的假设集——将扩展维格纳的朋友场景中的概率行为空间限制在了“局部友好性（LF）多面体”内，而量子关联原则上可以违反这些约束。
附：英文原文
Title: Local friendliness polytopes in multipartite scenarios
Author: Marwan Haddara* and Eric G. Cavalcanti†
Issue&Volume: 2025-01-09
Abstract: Recently, the local friendliness (LF) no-go theorem has attracted considerable interest due to its deep foundational implications. This no-go theorem applies to scenarios which combine Bell experiments with Wigners friend-type setups, containing spacelike separated superobservers assumed to be capable of performing quantum operations on a local observer, also known as their “friend.” The theorem shows that a set of assumptions termed “local friendliness”—weaker than the set of assumptions required for proving Bells theorem—constrains the space of probabilistic behaviors in extended Wigners friend scenarios to the “local friendliness (LF) polytope,” and that quantum correlations can, in principle, violate those constraints. In this work, we extend the study of local friendliness to multipartite scenarios—with arbitrary but finite numbers of superobservers, friends, measurements, and outcomes—and fully characterize the corresponding LF polytopes, their relationships with each other, with the Bell polytope, the no-signaling polytope, and the quantum set of correlations. In particular, we identify, via constructive proofs, all the canonical LF scenarios where the LF polytope coincides with the Bell polytope—hence identifying all the scenarios where “genuine LF inequalities” may arise. Among other results, we also show that whenever the LF polytope is distinct from the Bell and the no-signaling polytope, it also is neither contained in nor contains the quantum set of correlations. Apart from the foundational motivation of better understanding the constraints from local friendliness, our results may also find use in a priori unrelated contexts of device-independent information processing, where the LF polytopes have also been shown to arise, under the name of “partially deterministic polytopes.”
DOI: 10.1103/PhysRevA.111.012206
Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.012206
来源：科学网 小柯机器人
