Information and fidelity in projective measurements

TL;DR

This paper analyzes the information gained and fidelity preserved in projective measurements on unknown quantum states, revealing a tradeoff and discussing measurement efficiency in quantum information processing.

Contribution

It explicitly calculates information and fidelity for r-rank projective measurements on unknown states, highlighting a fundamental tradeoff and efficiency considerations.

Findings

Derived explicit formulas for information and fidelity in projective measurements.

Identified a tradeoff between information gain and fidelity at the single-outcome level.

Discussed measurement efficiency in the context of quantum state estimation.

Abstract

In this study, we explicitly calculate information and fidelity of an r-rank projective measurement on a completely unknown state in a d-dimensional Hilbert space. We also show a tradeoff between information and fidelity at the level of a single outcome and discuss the efficiency of measurement with respect to fidelity.