Information, fidelity, and reversibility in single-qubit measurements

TL;DR

This paper derives explicit formulas for information, fidelity, and reversibility in single-qubit measurements, revealing tradeoff relations at the level of individual measurement outcomes, which enhances understanding of quantum measurement processes.

Contribution

It provides a detailed analysis of measurement properties for arbitrary single-qubit measurements, focusing on outcome-specific tradeoff relations, a novel approach in quantum measurement theory.

Findings

Explicit formulas for information, fidelity, and reversibility as functions of measurement parameters.

Tradeoff relations between information gain, fidelity, and reversibility at the single-outcome level.

Results applicable to completely unknown quantum states in single-qubit systems.

Abstract

We explicitly calculate information, fidelity, and reversibility of an arbitrary single-qubit measurement on a completely unknown state. These quantities are expressed as functions of a single parameter, which is the ratio of the two singular values of the measurement operator corresponding to the obtained outcome. Thus, our results give information tradeoff relations to the fidelity and to the reversibility at the level of a single outcome rather than that of an overall outcome average.