Coherence of Superpositions

TL;DR

This paper investigates the coherence properties of superpositions of pure quantum states, establishing relationships and bounds that deepen understanding of quantum coherence in superposition states.

Contribution

It derives new relationships and bounds for the coherence of superpositions of pure states, including special cases with orthogonal supports.

Findings

When states have orthogonal support, the coherence difference is less than 1.

General cases have more complex but quantifiable relationships.

A lower bound for coherence of superpositions is established.

Abstract

Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the case that the two states have support on orthogonal subspaces, the relationship is simple, that is, the difference between the coherence of their superposition state and the average coherence of them is smaller than 1. In other cases, we obtain different and a little more complicated relationships. Furthermore, we also obtain the lower bound of coherence of superpositions.