Conclusive exclusion of quantum states
Conclusive exclusion of quantum states
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DOI：
10.1103/physreva.89.022336
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发表时间：
2014-02-25
影响因子：
2.9
通讯作者：
Perry, Christopher
中科院分区：
文献类型：
--
作者：
Bandyopadhyay, Somshubhro;Jain, Rahul;Perry, Christopher
在量子态排斥的任务中，我们考虑一个量子系统，它是从一个已知的集合中选择一个态来准备的。其目的是对系统进行测量，该系统可以最终裁定可能的准备程序的子集不可能发生。我们要问的是，为了使这一点成为可能，状态集必须服从什么条件，以及如果不服从，我们能完成任务的程度如何。量子态鉴别的任务形成了这组问题的一个子类。在本文中，我们制定的一般问题作为一个半定规划（SDP），使我们能够获得充分和必要条件的测量是最佳的。此外，我们得到了一个必要条件的排除是可以实现的确定性的状态集，我们给出了一个错误概率的下界的建设。由于Pusey，Barrett和Rudolph（PBR）的结果，这个最终排除状态的任务在量子力学基础的背景下变得重要。出于这一动机，我们使用我们的SDP推导出一个如何以及一类隐变量模型可以在一个特定的任务，证明模拟Tsirelson的约束的PBR实验和PBR在这个过程中给出的测量的最优性。我们还介绍了各种变化的结论性排除，包括明确的状态排除，状态排除与最坏情况下的错误。
In the task of quantum state exclusion, we consider a quantum system prepared in a state chosen from a known set. The aim is to perform a measurement on the system which can conclusively rule that a subset of the possible preparation procedures cannot have taken place. We ask what conditions the set of states must obey in order for this to be possible and how well we can complete the task when it is not. The task of quantum state discrimination forms a subclass of this set of problems. Within this paper, we formulate the general problem as a semidefinite program (SDP), enabling us to derive sufficient and necessary conditions for a measurement to be optimal. Furthermore, we obtain a necessary condition on the set of states for exclusion to be achievable with certainty, and we give a construction for a lower bound on the probability of error. This task of conclusively excluding states has gained importance in the context of the foundations of quantum mechanics due to a result from Pusey, Barrett, and Rudolph (PBR). Motivated by this, we use our SDP to derive a bound on how well a class of hidden variable models can perform at a particular task, proving an analog of Tsirelson's bound for the PBR experiment and the optimality of a measurement given by PBR in the process. We also introduce variations of conclusive exclusion, including unambiguous state exclusion, and state exclusion with worst-case error.