Sine distance for quantum states

TL;DR

This paper investigates the sine distance measure for quantum states, providing a thorough analysis and elementary proofs of its key properties, with applications to state-dependent cloning.

Contribution

It offers a comprehensive analysis of the sine distance for quantum states, including elementary proofs of its properties, expanding understanding of its role in quantum information tasks.

Findings

Proves key properties of the sine distance mathematically.

Clarifies the application of sine distance in quantum state cloning.

Enhances theoretical understanding of quantum state distinguishability.

Abstract

We thoroughly analyse the distance between quantum states that has been applied to state-dependent cloning and partly studied in the previous work of the author [Phys. Rev. A 66, 042304 (2002)]. Elementary proofs of its significant properties are given.