Correlation between resource-generating capacities of quantum gates

TL;DR

This paper investigates the relationship between the resource-generating capacities of quantum gates, focusing on how they generate quantum coherence and entanglement in two-qubit systems, revealing correlations and distribution profiles.

Contribution

It identifies the optimal basis for maximizing quantum coherence and explores the correlation between coherence and entanglement generation in quantum gates.

Findings

High coherence generating gates are often high entanglement generating gates.

The distribution of entanglement for fixed coherence differs from that of fixed entanglement for coherence.

Both distributions follow a beta distribution pattern.

Abstract

We analyze the optimal basis for generating the maximum relative entropy of quantum coherence by an arbitrary gate on a two-qubit system. The optimal basis is not unique, and the high quantum coherence generating gates are also typically high entanglement generating ones and vice versa. However, the profile of the relative frequencies of Haar random unitaries generating different amounts of entanglement for a fixed amount of quantum coherence is different from the one in which the roles of entanglement and quantum coherence are reversed, although both follow the beta distribution.