Testing quantum states for purity
Testing quantum states for purity
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测试量子态的纯度
DOI：
10.1111/j.1467-9876.2012.01040.x
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Aron Pasieka
中科院分区：
文献类型：
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作者：
P. Jupp;P. Kim;J. Koo;Aron Pasieka
有限量子系统的最简单态是纯态。本文的动机是需要测试统计是否一个给定的物理状态是纯的。由于纯状态位于所有状态集合的边界上，因此不满足通常的正则性条件，该正则性条件证明标准大样本近似于偏差和得分统计量的零分布是合理的。对于产生泊松计数数据的大类量子实验，本文使用所有状态的参数空间的扩大来开发似然比和纯度的得分测试。相应统计量的渐近零分布为χ2。测试说明了一些量子实验的分析，涉及酉可纠正的代码。
Summary. The simplest states of finite quantum systems are the pure states. The paper is motivated by the need to test statistically whether or not a given physical state is pure. Because the pure states lie in the boundary of the set of all states, the usual regularity conditions that justify the standard large sample approximations to the null distributions of the deviance and the score statistic are not satisfied. For a large class of quantum experiments that produce Poisson count data, the paper uses an enlargement of the parameter space of all states to develop likelihood ratio and score tests of purity. The asymptotic null distributions of the corresponding statistics are χ2. The tests are illustrated by the analysis of some quantum experiments involving unitarily correctable codes.