Quantifying coherence with principal diagonal elements of density matrix

TL;DR

This paper introduces a new, simple measure of quantum coherence based on the principal diagonal elements of the density matrix, demonstrating its effectiveness and advantages over existing measures in pure states.

Contribution

The paper proposes the Principal Diagonal Difference of Coherence (C_PDD), a novel, easy-to-evaluate coherence quantifier that is non-negative, self-normalized, and monotonic, with validated superiority in pure states.

Findings

C_PDD is better correlated with coherence evolution than traditional measures.

C_PDD is non-negative, self-normalized, and monotonic under incoherent operations.

Diagonal elements of the density matrix contain complete information on pure state coherence.

Abstract

Being the key resource in quantum physics, the proper quantification of coherence is of utmost importance. Amid complex-looking functionals in quantifying coherence, we set forth a simple and easy-to-evaluate approach: Principal diagonal difference of coherence (C_PDD), which we prove to be non-negative, self-normalized, and monotonic (under any incoherent operation). To validate this theory, we thought of a fictitious two-qubit system (both interacting and non-interacting) and, through the laser pulse-system interaction (semi-classical approach), compare the coherence evolution of C_PDD with the relative entropy of coherence (C_(r.e)) and l_1-norm of coherence (C_(l_1 )), in a pure-state regime. The numerical results show that the response of C_PDD is better than the other two quantifiers. To the best of our knowledge, this letter is the first to show that a set of density-matrix diagonal elements carries complete information on the coherence (or superposition) of any pure quantum state.