| （英） |
For distinguishing quantum states sampled from a fixed ensemble, the gap in bipartite and single-party distinguishability can be interpreted as a {¥it 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 $N$-{¥it 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 {¥it parallel repetition conjecture} of {¥it 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. |