Quantumness of Relative Incompatibility

TL;DR

This paper introduces a new measure called quantumness of relative incompatibility, based on relative entropy, to quantify the non-classical features of quantum states with respect to non-commuting observables, revealing deeper quantum properties beyond coherence.

Contribution

It proposes a novel measure of quantumness based on relative entropy of marginal distributions, exploring its relation to quantum coherence and complementarity.

Findings

The measure satisfies basic axioms of quantumness.

It depicts complementarity with quantum coherence.

The measure reveals inherent quantum features beyond coherence.

Abstract

We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is inconsequential, hence probability distribution of outcomes of any observable remains undisturbed. We define relative entropy of the two marginal probability distributions as a measure of quantumness in the state, which is revealed only in presence of two non-commuting observables. Like all other measures, we show that the proposed measure satisfies some basic axioms. Also, we find that this measure depicts complementarity with quantum coherence. The relation is more vivid when we choose one of the observables in such a way that its eigen basis matches with the basis in which the coherence is measured. Our result indicates that the quantumness in a single system is still an interesting question to explore and there can be an inherent feature of the state which manifests beyond the idea of quantum coherence.