Local simultaneous state discrimination

Quantum state discrimination is one of the most fundamental problems in quantum information theory, with applications ranging from channel coding to metrology and cryptography. In this work, we introduce a variant of this task: local simultaneous state discrimination (LSSD). While previously studied distributed variants of state discrimination allowed some communication between the parties to come up with a joint answer, in LSSD they cannot communicate and have to simultaneously answer correctly. We illustrate by multiple examples that this problem significantly differs from single-party state discrimination, even when the states are completely classical. We show that an additional entangled resource can increase the optimal success probability in LSSD, and stronger-than-quantum no-signaling resources can allow for an even higher success probability. We also show that finding the optimal strategy in (classical) three-party LSSD is NP-hard. Furthermore, we provide an example of symmetric LSSD for which the optimal strategy is not symmetric, and prove a sufficient condition for the existence of an optimal symmetric strategy. While interesting in its own right, the LSSD problem also arises in quantum cryptography. In particular, we explore the connections between the problem of unclonable encryption and LSSD. We give an explicit cloning-indistinguishable attack that succeeds with probability $1/2+\mu /16$ where $\mu$ is related to the largest eigenvalue of the resulting quantum ciphertext states.