Information, fidelity, and reversibility in general quantum measurements

TL;DR

This paper analyzes the relationships between information gain, fidelity, and reversibility in quantum measurements, providing formulas based on measurement operator singular values and exploring tradeoffs for specific measurement classes.

Contribution

It introduces a framework to quantify information, fidelity, and reversibility in quantum measurements using singular values, highlighting outcome-specific tradeoffs.

Findings

Quantitative expressions for information, fidelity, and reversibility based on measurement singular values

Tradeoff analysis among these quantities for measurements with degenerate singular values

Outcome-specific tradeoffs rather than average-based results

Abstract

We present the amounts of information, fidelity, and reversibility obtained by arbitrary quantum measurements on completely unknown states. These quantities are expressed as functions of the singular values of a measurement operator corresponding to the obtained outcome. As an example, we consider a class of quantum measurements with highly degenerate singular values to discuss tradeoffs among information, fidelity, and reversibility. The tradeoffs are at the level of a single outcome, in the sense that the quantities pertain to each single outcome rather than the average over all possible outcomes.