基于正贝叶斯证据的状态和信道排序
Ordering states and channels based on positive Bayesian evidence
摘要：
在本文中，我们引入了一个新的偏序的量子态，认为哪些国家可以实现从其他更新的“同意”贝叶斯证据。我们证明，这种顺序也可以解释在最坏情况下distuinguishability状态之间使用量子最大发散的概念。这个顺序解决了哪些状态是它们更纯的对应物的最佳近似的问题，并且它以明确的方式表明，贝叶斯规则的拟议量子模拟导致贝叶斯更新，当更新积极证据时，尽可能少地改变状态。我们证明了一些结构性质的顺序，特别是为了保持凸混合和张量积的状态，它是一个域。给出了这些性质的阶的唯一性。最后，我们利用Jamiolkowski同构将这种态的序推广到量子信道上。这种顺序将单位/非单位保迹量子信道的空间变成域，与信道上的规则顺序不同，域对于单位保迹信道来说不是平凡的。
英文摘要：
In this paper we introduce a new partial order on quantum states that considers which states can be achieved from others by updating on `agreeing' Bayesian evidence. We prove that this order can also be interpreted in terms of minimising worst case distuinguishability between states using the concept of quantum max-divergence. This order solves the problem of which states are optimal approximations to their more pure counterparts and it shows in an explicit way that a proposed quantum analogue of Bayes' rule leads to a Bayesian update that changes the state as little as possible when updating on positive evidence. We prove some structural properties of the order, specifically that the order preserves convex mixtures and tensor products of states and that it is a domain. The uniqueness of the order given these properties is discussed. Finally we extend this order on states to one on quantum channels using the Jamiolkowski isomorphism. This order turns the spaces of unital/non-unital trace-preserving quantum channels into domains that, unlike the regular order on channels, is not trivial for unital trace-preserving channels.
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