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Pure States of Maximum Uncertainty with Respect to a Given POVM
Open Systems & Information Dynamics ( IF 0.8 ) Pub Date : 2020-05-05 , DOI: 10.1142/s123016122050002x
Anna Szymusiak 1
Affiliation  

One of the differences between classical and quantum world is that in the former we can always perform a measurement that gives certain outcomes for all pure states, while such a situation is not possible in the latter one. The degree of randomness of the distribution of the measurement outcomes can be quantified by the Shannon entropy. While it is well known that this entropy, as a function of quantum states, needs to be minimized by some pure states, we would like to address the question how ‘badly’ can we end by choosing initially any pure state, i.e., which pure states produce the maximal amount of uncertainty under given measurement. We find these maximizers for all highly symmetric POVMs in dimension 2, and for all SIC-POVMs in any dimension.

中文翻译:

关于给定 POVM 的最大不确定性纯状态

经典世界和量子世界之间的区别之一是,在前者中,我们总是可以对所有纯态进行某种测量,而这种情况在后者中是不可能的。测量结果分布的随机程度可以通过香农熵来量化。虽然众所周知,作为量子态的函数,这种熵需要被一些纯态最小化,但我们想通过最初选择任何纯态来解决这个问题,例如状态在给定测量下产生最大量的不确定性。我们为维度 2 中所有高度对称的 POVM 以及任何维度中的所有 SIC-POVM 找到了这些最​​大化器。
更新日期:2020-05-05
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