Local simultaneous state discrimination

TL;DR

This paper introduces Local Simultaneous State Discrimination (LSSD), a new quantum information task where parties must simultaneously identify states without communication, revealing complex strategic differences and computational hardness.

Contribution

The work defines LSSD, explores its properties, shows entanglement and non-signalling resources can enhance success, and proves the problem's NP-hardness for three parties.

Findings

Optimal local discrimination strategies differ from LSSD strategies.

Entanglement can increase success probability in LSSD.

Non-signalling resources outperform entanglement in some cases.

Abstract

Quantum state discrimination is one of the most fundamental problems studied in quantum information theory. Applications range from channel coding to metrology and cryptography. In this work, we introduce a new variant of this task: Local Simultaneous State Discrimination (LSSD). While previous distributed variants of the discrimination problem always allowed some communication between the parties to come up with a joint answer, the parties in LSSD cannot communicate and have to simultaneously answer correctly. This simultaneity implies, e.g., that for classical states, the problem does not trivialize to a non-distributed distinguishing task. While interesting in its own right, this problem also arises in quantum cryptography. After introducing the problem, we give a number of characterization results. We give examples showing that i) the optimal strategy for local discrimination need not coincide with the optimal strategy for LSSD, even for classical states, ii) an additional entangled resource can increase the optimal success probability in LSSD, and iii) stronger-than-quantum non-signalling resources can allow for a higher success probability in some cases, compared to strategies using entanglement. Finally, we show that finding the optimal strategy in (classical) 3-party LSSD is NP-hard.