Metrics Of Quantum States

TL;DR

This paper explores generalized metrics for quantum states, proving their convexity and contractivity, which aids in understanding quantum state geometry and entanglement detection.

Contribution

It introduces generalized quantum state metrics extending trace and Bures metrics, with proofs of their convexity and contractivity properties.

Findings

Metrics are joint convex and contractive under quantum operations

Results facilitate studying quantum state geometry

Metrics are useful for entanglement detection

Abstract

In this paper, we study metrics of quantum states. These metrics are natural generalization of trace metric and Bures metric. We will prove that the metrics are joint convex and contractive under quantum operation. Our results can find important application in studying the geometry of quantum states and is useful to detect entanglement.