Sequential Quantum Maximum Confidence Discrimination

TL;DR

This paper explores sequential quantum state discrimination with maximum confidence, revealing conditions for optimal measurements and a tradeoff between information gain and disturbance, advancing understanding of quantum measurement strategies.

Contribution

It introduces a framework for sequential maximum-confidence quantum state discrimination and identifies conditions for achieving equal confidence levels across parties.

Findings

Sequential discrimination with equal confidence requires linearly independent measurement operators.

A tradeoff exists: less information gain per measurement allows more parties to participate.

Maximum-confidence discrimination generalizes other quantum state discrimination strategies.

Abstract

Sequential quantum information processing may lie in the peaceful coexistence of no-go theorems on quantum operations, such as the no-cloning theorem, the monogamy of correlations, and the no-signalling principle. In this work, we investigate a sequential scenario of quantum state discrimination with maximum confidence, called maximum-confidence discrimination, which generalizes other strategies including minimum-error and unambiguous state discrimination. We show that sequential state discrimination with equally high confidence can be realized only when positive-operator-valued measure elements for a maximum-confidence measurement are linearly independent; otherwise, a party will have strictly less confidence in measurement outcomes than the previous one. We establish a tradeoff between the disturbance of states and information gain in sequential state discrimination, namely, that the less a party learn in state discrimination in terms of a guessing probability, the more parties can participate in the sequential scenario.