Bipartite discrimination of independently prepared quantum states as a counterexample to a parallel repetition conjecture

TL;DR

This paper demonstrates that bipartite quantum state discrimination exhibits asymptotic nonlocality disappearance under certain conditions, providing a counterexample to a parallel repetition conjecture in theoretical computer science.

Contribution

It introduces a novel bipartite state discrimination scenario that challenges the parallel repetition conjecture by showing nonlocality vanishes asymptotically with concentrated distributions.

Findings

Success probability approaches 1 as N increases when entropy < 1.

Nonlocality asymptotically disappears for concentrated distributions.

Counterexample to the parallel repetition conjecture in interactive games.

Abstract

For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a nonlocality of the ensemble. In this paper, we consider bipartite state discrimination in a composite system consisting of $N$ subsystems, where each subsystem is shared between two parties and the state of each subsystem is randomly sampled from a particular ensemble comprising the Bell states. We show that the success probability of perfectly identifying the state converges to $1$ as $N\rightarrow\infty$ if the entropy of the probability distribution associated with the ensemble is less than $1$, even if the success probability is less than $1$ for any finite $N$. In other words, the nonlocality of the $N$-fold ensemble asymptotically disappears if the probability distribution associated with each ensemble is concentrated. Furthermore, we show that the disappearance of the nonlocality can be regarded as a remarkable counterexample of a fundamental open question in theoretical computer science, called a parallel repetition conjecture of interactive games with two classically communicating players. Measurements for the discrimination task include a projective measurement of one party represented by stabilizer states, which enable the other party to perfectly distinguish states that are sampled with high probability.