Uncertainty and certainty relations for quantum coherence with respect to design-structured POVMs

TL;DR

This paper derives uncertainty and certainty relations for quantum coherence measured by relative entropy, specifically with respect to design-structured POVMs, enhancing understanding of coherence in quantum information protocols.

Contribution

It introduces new uncertainty and certainty relations for quantum coherence relative to design-structured POVMs, a novel approach in quantum measurement analysis.

Findings

Relations are exemplified with quantum designs in two-dimensional space.

Provides bounds for coherence with respect to structured POVMs.

Enhances understanding of coherence behavior in quantum measurements.

Abstract

The concept of quantum coherence and its possible use as a resource are currently the subject of active researches. Uncertainty and complementarity relations for quantum coherence allow one to study its changes with respect to other characteristics of the process of interest. Protocols of quantum information processing often use measurements that have a special inner structure. Quantum designs are considered as tools with a perspective of fruitful applications in quantum information processing. We obtain uncertainty and certainty relations for coherence averaged with respect to a set of design-structured POVMs of rank one. To characterize the degree of coherence, the relative entropy of coherence is utilized. The derived relations are exemplified with quantum designs in the two-dimensional Hilbert space.