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arXiv · 1607.08000

Distribution of Standard deviation of an observable among superposed states

Chang-shui Yu·Ting-ting Shao·Dong-mo Li
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Abstract

The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a superposition state is distributed.

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Chang-shui Yu, Ting-ting Shao, Dong-mo Li. 2016-07-27. Distribution of Standard deviation of an observable among superposed states. https://doi.org/10.1016/j.aop.2016.06.017

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