Quantifying quantum coherence and the deviation from the total probability formula

TL;DR

This paper introduces a new way to quantify quantum coherence based on deviations from the total probability formula, offering an alternative to resource-theoretic measures and revealing basis-dependent properties.

Contribution

It proposes a coherence measure rooted in ontological considerations, differing from existing resource theory approaches, and analyzes its basis dependence and relation to purity.

Findings

The new coherence measure satisfies a distinct set of axioms from previous measures.

The l2-coherence norm depends on the basis and is well approximated by the square root of the purity.

The approach emphasizes the foundational role of the total probability formula in quantum coherence.

Abstract

We propose a novel approach to quantify quantum coherence which, contrary to the previous ones, does not rely on resource theory but rather on ontological considerations. In this framework, coherence is understood as the ability for a quantum system's statistics to deviate from the total probability formula. After motivating the importance of the total probability formula in quantum foundations, we propose a new set of axioms that a measure of coherence should satisfy, and show that it defines a class of measures different from the main previous proposal. Finally, we prove a general result about the dependence of the l2-coherence norm on the basis of interest, and show that it is well approximated by the square root of the purity in most bases.