Fidelity induced distance measures for quantum states

TL;DR

This paper introduces new fidelity-based distance measures for quantum states, explores their properties, and connects them with existing metrics like trace, Sine, and Bures metrics for qubits and qudits.

Contribution

It proposes novel fidelity-induced metrics for quantum states and analyzes their mathematical properties and relationships with established quantum state metrics.

Findings

New fidelity-based metrics for quantum states are introduced.

The connection between the new metrics and existing metrics is established for qubits.

Properties like CPT contractiveness and joint convexity are demonstrated.

Abstract

Fidelity plays an important role in quantum information theory. In this letter, we introduce new metric of quantum states induced by fidelity, and connect it with the well-known trace metric, Sine metric and Bures metric for the qubit case. The metric character is also presented for the qudit (i.e., $d$-dimensional system) case. The CPT contractive property and joint convex property of the metric are also studied.