发表机构
Oxford Quantum Circuits（牛津量子电路）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了Shor关于量子二分体可获取信息的猜想，通过初等证明、显式构造更优投影测量及凸优化表述，解决了长期开放问题。
AI 中文摘要
任意给定量子系综的可获取信息量化了通过任何量子测量从该系综中能提取的Shannon信息的最大量。近三十年前，Shor猜想任何量子二分体（即两个态的系综）的可获取信息可通过投影测量达到。最近，Keil发表了仅限于量子比特情形下该猜想的证明。在此，我们决定性地解决了这个长期悬而未决的问题。首先，我们证明Shor猜想在任意维度下可由Fang、Fawzi和Fawzi最近的结果推出，并给出一个自包含的初等证明。其次，对于任意给定的二分体和测量，我们提供了一种投影测量的显式构造，该投影测量在从给定二分体提取信息方面优于该测量。第三，虽然可获取信息的计算通常已知是非凸的，但我们把二分体可获取信息的计算表述为一个凸问题。
英文摘要
The accessible information of any given quantum ensemble quantifies the maximum amount of Shannon information that can be extracted from the ensemble by any quantum measurement. Almost three decades ago, Shor conjectured that the accessible information of any quantum dichotomy, that is, an ensemble of two states, is attained by a projective measurement. Recently, a proof of this conjecture restricted to the qubit case was published by Keil. Here, we conclusively settle this longstanding open problem. First, we show that Shor's conjecture follows, in arbitrary dimension, from a recent result by Fang, Fawzi and Fawzi, and we provide a self-contained, elementary proof. Second, for any given dichotomy and measurement, we provide the explicit construction of a projective measurement that outperforms such a measurement in extracting information from the given dichotomy. Third, while the computation of the accessible information is known to be non-convex in general, we frame the computation of the accessible information of dihotomies as a convex problem.
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