Some properties of partial fidelities

TL;DR

This paper explores the fundamental properties of Uhlmann's partial fidelities, establishing their statistical interpretation, multiplicativity, and relation to trace distances, highlighting their robustness as quantum state distinguishability measures.

Contribution

It provides a comprehensive analysis of partial fidelities, including their statistical meaning, multiplicativity, and invariance under certain quantum operations, advancing understanding of quantum state comparison tools.

Findings

Partial fidelities have a clear statistical interpretation via POVM measurements.

They are multiplicative under tensor products.

Partial fidelities do not decrease under unistochastic quantum operations.

Abstract

Basic properties of Uhlmann's partial fidelities are discussed. Statistical interpretation in terms of POVM measurements is established. Multiplicativity properties are considered. The relationship between partial fidelities and partitioned trace distances is derived. As it is shown, the partial fidelities cannot decrease under unistochastic quantum operations. Thus, the partial fidelities have good properties in the sense of their use as distinguishability measures.