发表机构
Scuola Normale Superiore; Freie Universität Berlin; University of Nottingham（高等师范学校; 柏林自由大学; 诺丁汉大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对受限集体高斯测量下的多模玻色子高斯态，建立了 Stein 指数的单字母公式，揭示第一、第二矩的渐近解耦，并排除中心高斯态下集体测量的优势。
AI 中文摘要
量子信息中一个核心而神秘的问题是在受限测量下量子态的渐近可区分性。这里我们研究在任意集体高斯测量限制下，一般多模玻色子高斯态的非对称渐近假设检验。我们为许多态对建立了 Stein 指数的单字母公式，该公式包含两个不同的贡献，分别对应于第一矩和第二矩。值得注意的是，高斯测量的相对熵表现出真正的非可加性，但可加性违反的唯一效应是使第一矩和第二矩在渐近上解耦。我们通过新颖的对数行列式矩阵不等式建立第二矩项可加性的充分条件来证明这一点。我们的结果不仅在实际广泛情形中确定了高斯 Stein 指数的单字母表达式，而且排除了在考虑中心高斯态时集体高斯测量可能带来的任何优势。
英文摘要
A central yet mysterious problem in quantum information is the asymptotic distinguishability of quantum states under restricted measurements. Here we look at asymptotic asymmetric hypothesis testing for general multi-mode bosonic Gaussian states restricted to arbitrary collective Gaussian measurements. We establish a single-letter formula for the Stein exponent for many pairs of states, featuring two distinct contributions, corresponding to first and second moments, respectively. Remarkably, the Gaussian-measured relative entropy exhibits genuine non-additivity, but the only effect of additivity violations is to asymptotically decouple first and second moments. We prove this by establishing sufficient conditions for additivity of the second-moment term via novel log-determinant matrix inequalities. Our results not only identify a single-letter expression for the Gaussian Stein exponent in a wide range of practical situations, but also rule out any possible advantage from collective Gaussian measurements when considering centred Gaussian states.
Comments5 + 12 pages, 1 figure
