Generalized bipartite quantum state discrimination problems with sequential measurements
Generalized bipartite quantum state discrimination problems with sequential measurements
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DOI：
10.1103/physreva.97.022340
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发表时间：
2017-07
影响因子：
2.9
通讯作者：
K. Nakahira;Kentaro Kato;T. Usuda
中科院分区：
文献类型：
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作者：
K. Nakahira;Kentaro Kato;T. Usuda
我们研究了一个寻找量子序贯测量的优化问题，它形成了一个广泛的一类状态判别问题的限制，只允许序贯测量。序列测量从爱丽丝到鲍勃的二分系统被认为是。利用这一事实，即优化问题可以制定为一个问题，只有爱丽丝的测量，是凸规划，我们推导出它的对偶问题和最优解的充分必要条件。在我们解决的问题中，爱丽丝的测量的输出可以是无限的或连续的，而被认为是具有有限数量的结果的连续测量。结果表明，存在一个最佳的顺序测量，其中爱丽丝的测量与有限数量的结果，只要一个解决方案存在。我们还表明，如果问题具有一定的对称性，那么存在一个最优解具有相同类型的对称性。一个极小极大版本的问题被认为是，并推导出一个极小极大解决方案的必要和充分条件。最后给出了一个例子，其中我们的结果可以用来获得一个最佳的顺序测量的解析表达式。
We investigate an optimization problem of finding quantum sequential measurements, which forms a wide class of state discrimination problems with the restriction that only sequential measurements are allowed. Sequential measurements from Alice to Bob on a bipartite system are considered. Using the fact that the optimization problem can be formulated as a problem with only Alice's measurement and is convex programming, we derive its dual problem and necessary and sufficient conditions for an optimal solution. In the problem we address, the output of Alice's measurement can be infinite or continuous, while sequential measurements with a finite number of outcomes are considered. It is shown that there exists an optimal sequential measurement in which Alice's measurement with a finite number of outcomes as long as a solution exists. We also show that if the problem has a certain symmetry, then there exists an optimal solution with the same type of symmetry. A minimax version of the problem is considered, and necessary and sufficient conditions for a minimax solution are derived. An example in which our results can be used to obtain an analytical expression for an optimal sequential measurement is finally provided.