Maximum coherence in the optimal basis

TL;DR

This paper analytically determines the maximum quantum coherence achievable by optimizing the basis, emphasizing the critical role of mutually unbiased bases (MUBs) across various coherence measures, especially for pure or single-qubit states.

Contribution

It provides analytical solutions for maximum coherence via basis optimization and highlights the universal optimality of MUBs for multiple coherence measures in specific states.

Findings

MUBs are optimal for maximum coherence in various measures.

Analytical solutions for maximum coherence are obtained.

Upper bounds for the $l_1$ norm of coherence are discussed.

Abstract

The resource theoretic measure of quantum coherence is basis dependent, and the amount of coherence contained in a state is different in different bases. We obtained analytical solutions for the maximum coherence by optimizing the reference basis and highlighted the essential role of the mutually unbiased bases (MUBs) on attaining the maximum coherence. Apart from the relative entropy of coherence, we showed that the MUBs are optimal for the robustness of coherence, the coherence weight, and the modified skew information measure of coherence for any state. Moreover, the MUBs are optimal for all the faithful coherence measures if the state is pure or is of the single qubit. We also highlighted an upper bound for the $l_1$ norm of coherence and compared it with the other bounds as well as the maximum one attainable by optimizing the reference basis.