Distribution of Standard deviation of an observable among superposed states
arXiv:1607.08000 · doi:10.1016/j.aop.2016.06.017
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.
arXiv comment14 pages, 3 figures, misprints are revised
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