信息因果性不能唯一确定量子关联集合
Information causality does not single out the set of quantum correlations
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中文总结 AI 辅助
本文证明信息因果性原理无法唯一确定量子关联集合：在有限数据库长度下及3输入2输出贝尔场景中，均存在满足IC但包含后量子关联的集合，从而否定了IC作为量子关联完整特征的可能性。
中文摘要 AI 辅助
信息因果性（IC）被引入作为一条物理原理，对贝尔场景中两方（Alice和Bob）之间的非局域关联施加约束。具体而言，它指出Bob能够获得的关于Alice持有的$n$比特数据库的信息量受限于她向他通信的信息量。迄今为止，对于任意$n \in \mathbb{N}$，IC是否能唯一确定量子关联集合的问题仍然悬而未决，这意味着尚不清楚对于两方的任意输入数$m$和输出数$d$，满足IC的关联集合是否恰好与量子关联一致。在本工作中，我们对这一问题给出了否定回答。首先，我们证明对于任意有限数据库长度$n \geq 2$，存在一个二分关联集合，它满足所有兼容协议的IC，并在每方具有$n+1$个输入和$2$个输出的贝尔场景中展现出后量子关联。这一结果依赖于为GPTs构建一个熵证明的IC，该证明可能具有独立的意义。我们进一步证明，在每方具有$n+1$个输入和$2$个输出的贝尔场景中，我们构建的关联集合既不是量子关联的超集也不是其子集。其次，我们在每方具有$3$个输入和$2$个输出的贝尔场景中构建了一个关联集合，它满足IC（对于所有数据库大小$n \in \mathbb{N}$），并且包含后量子点。因此，所有已知的信息因果性表述都未能完全刻画二分量子关联集合，即使在$3$输入、$2$输出的贝尔场景中也是如此。
英文摘要
Information causality (IC) was introduced as a physical principle that imposes constraints on the non-local correlations between two parties (Alice and Bob) in a Bell scenario. Specifically, it states that the information that Bob can gain about an $n$-bit database held by Alice is bounded by the information she communicates to him. To date, the question whether IC for any $n \in \mathbb{N}$ singles out the set of quantum correlations remains open, meaning that it is unknown whether for any number of inputs $m$ and outputs $d$ of the two parties the set of correlations that satisfy IC exactly coincides with the quantum correlations. In this work, we answer this question in the negative. Firstly, we show that for any finite database length $n \geq 2$, there is a bipartite set of correlations that satisfies IC for all compatible protocols and that exhibits post-quantum correlations in the Bell scenario with $n+1$ inputs and $2$ outcomes per party. This result relies on constructing an entropic proof of IC for GPTs that may be of independent interest. We further show that in the Bell scenario with $n+1$ inputs and $2$ outcomes per party, our constructed sets of correlations lead to neither a superset nor a subset of the quantum correlations. Secondly, we construct a set of correlations in the Bell scenario with $3$ inputs and $2$ outputs per party that satisfies IC (for all database sizes $n \in \mathbb{N}$) and that includes post-quantum points. Consequently, all known formulations of information causality fail to fully characterize the bipartite set of quantum correlations, already in the $3$-input, $2$-outcome Bell scenario.
发表机构
- Inria, Télécom Paris – LTCI, Institut Polytechnique de Paris（法国国家信息与自动化研究所，巴黎电信学院-信号与系统实验室，巴黎理工学院）
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