复合量子系统的无影响态
Influence-free states on compound quantum systems
摘要：
让Alice和Bob能够进行局部量子测量并进行经典通信。这种测量的数学上一致的联合概率分配（"状态“）的集合适当地大于Alice-Bob系统的量子力学混合状态的集合。它规范同构于从Alice空间上的有界线性算子到Bob空间上的有界线性算子的正（不一定是完全正）线性映射集Phi，其中Tr Phi（I）=1。我们回顾了这样一个事实，即允许经典通信相当于在与通信相反的方向上执行“无瞬时信号”（“无影响”）。我们建立了在"可分解“态的子类中，即正态与部分转置为正的“PTP”态的凸组合中，极值态就是极值正态和极值PTP态。我们表明，两个这样的状态，由相同的一对缔约方，不一定被组合为独立的状态（他们的张量积），如果全套的量子操作是允许本地的每一方。我们使用的“测试空间”的框架和国家对这些，适合展示类比和偏离的经验概率理论从经典概率论。这导致了对量子力学和贝叶斯概率论之间类比的更深入理解。测量后更新状态的“最贝叶斯”量子规则的存在，以及它与通过测量一个系统获得另一个系统的信息的情况的关联，是一个一般命题的情况，适用于无信号要求的组合测试空间。
英文摘要：
Let Alice and Bob be able to make local quantum measurements and communicate classically. The set of mathematically consistent joint probability assignments (``states'') for such measurements is properly larger than the set of quantum-mechanical mixed states for the Alice-Bob system. It is canonically isomorphic to the set of positive (not necessarily completely positive) linear maps Phi from the bounded linear operators on Alice's space to those on Bob's, for which Tr Phi(I)=1. We review the fact that allowing classical communication is equivalent to enforcing ``no-instantaneous-signalling'' (``no--influence'') in the direction opposite the communication. We establish that in the subclass of ``decomposable'' states, i.e. convex combinations of positive states with "PTP" ones whose partial transpose is positive, the extremal states are just the extremal positive and extremal PTP states. We show that two such states, shared by the same pair of parties, cannot necessarily be combined as independent states (their tensor product) if the full set of quantum operations is allowed locally to each party. We use a framework of ``test spaces'' and states on these, suited for exhibiting the analogies and deviations of empirical probabilistic theories from classical probability theory. This leads to a deeper understanding of analogies between quantum mechanics and Bayesian probability theory. The existence of a ``most Bayesian'' quantum rule for updating states after measurement, and its association with the situation when information on one system is gained by measuring another, is a case of a general proposition holding for test spaces combined subject to the no-signalling requirement.
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