All classes of informationally complete symmetric measurements in finite dimensions

TL;DR

This paper introduces a broad class of symmetric measurements that generalize known quantum measurement frameworks, providing new tools for quantum information tasks such as entropic relations and entanglement detection.

Contribution

It presents a unified framework for symmetric informationally complete measurements and mutually unbiased symmetric measurements in finite dimensions, including construction methods and examples.

Findings

Introduces a broad class of informationally complete symmetric measurements.

Provides a general construction method for new measurement families.

Analyzes properties and applications in entropic relations and entanglement detection.

Abstract

A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural way to define two new families of mutually unbiased symmetric measurement operators in any finite dimension. We show a general method of their construction, together with an example of an optimal measurement. Finally, we analyze the properties of symmetric measurements and provide applications in entropic relations and entanglement detection.