Distribution of Standard deviation of an observable among superposed states

TL;DR

This paper investigates how the standard deviation of an observable distributes among superposed quantum states, establishing bounds that relate to coherence and observable incompatibility.

Contribution

It introduces bounds on the SD distribution in superpositions and links these bounds to quantum coherence and observable incompatibility.

Findings

SD of superposition bounded by SDs of component states

Bounds serve as measures of quantum coherence

Distribution of incompatibility among superposed states

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.