Quantifying coherence with principal diagonal elements of density matrix

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.