Optimal quantum state discrimination with confidentiality

TL;DR

This paper presents a protocol for optimal quantum state discrimination that ensures confidentiality among multiple observers, preventing any subset of fewer than all observers from gaining information about the state.

Contribution

It introduces a secure quantum measurement protocol for symmetric state sets, enabling optimal discrimination while maintaining confidentiality among observers.

Findings

Protocol achieves optimal inconclusive measurements.

Ensures no information leakage to fewer than all observers.

Applicable to symmetric, Abelian geometrically uniform states.

Abstract

We investigate quantum state discrimination with confidentiality. $N$ observers share a given quantum state belonging to a finite set of known states. The observers want to determine the state as accurately as possible and send a discrimination result to a receiver. However, the observers are not allowed to get any information about which state was given. $N-1$ or fewer observers might try to steal the information, but if $N$ observers coexist, the honest ones will keep the dishonest ones from doing anything wrong. Assume that the state set has a certain symmetry, or more precisely, is Abelian geometrically uniform; this letter describes the case of three linearly independent cyclic pure states as a special case. We propose a protocol that realizes any optimal inconclusive measurement, which is a generalized version of a minimum-error measurement and an optimal unambiguous measurement, for such a state set and ensures that any combined state of $N-1$ or fewer observers has absolutely no information about the given state. Our protocol provides a method of performing a quantum measurement securely, which could be useful in quantum information applications.