Quantifying coherence with principal diagonal elements of density matrix

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 (CPDD), which we prove to be non-negative, self-normalized, and monotonic (under any incoherent operation). In an attempt to extend CPDD in the domain of mixed states, we propose a simple, generic expression (applicable to other pure state coherence measures as well). To validate this theory, we consider 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 CPDD with the relative entropy of coherence (Cr⋅e) and the l1-norm of coherence (Cl1), in both pure- and mixed-state regimes. The results from both the numerical and analytical (for a two-level system) studies clearly demonstrate a better sensitivity of CPDD in the close proximity of the maximally coherent states (MCS) than Cr⋅e or Cl1. To the best of our knowledge, CPDD is the only quantifier (among all existing coherence quantifiers) that is a linear function of density-matrix elements.