Frobenius-norm-based measures of quantum coherence and asymmetry

TL;DR

This paper introduces Frobenius-norm-based measures for quantum coherence and asymmetry, linking them to purity and quantum correlations, and explores their properties and implications for quantum systems.

Contribution

It develops new Frobenius-norm-based measures for quantum coherence and asymmetry, providing explicit physical interpretations and analyzing their behavior under various quantum transformations.

Findings

The coherence measure is basis-independent and related to quantum purity.

Collective SU(2) transformations significantly affect asymmetry in N-qubit systems.

Quantum correlations influence the asymmetry measures under local and collective operations.

Abstract

We formulate the Frobenius-norm-based measures for quantum coherence and asymmetry respectively. In contrast to the resource theory of coherence and asymmetry, we construct a natural measure of quantum coherence inspired from optical coherence theory while the group theoretical approach is employed to quantify the asymmetry of quantum states. Besides their simple structures and explicit physical meanings, we observe that these quantities are intimately related to the purity (or linear entropy) of the corresponding quantum states. Remarkably, we demonstrate that the proposed coherence quantifier is not only a measure of mixedness, but also an intrinsic (basis-independent) quantification of quantum coherence contained in quantum states, which can also be viewed as a normalized version of Brukner-Zeilinger invariant information. In our context, the asymmetry of N-qubit quantum systems is considered under local independent and collective SU(2) transformations. Intriguingly, it is illustrated that the collective effect has a significant impact on the asymmetry measure, and quantum correlation between subsystems plays a non-negligible role in this circumstance.