Time-Constrained Local Quantum State Discrimination

Inspired by protocols in relativistic quantum cryptography, we investigate quantum state discrimination using local operations and simultaneous classical or quantum communication (LOSCC/LOSQC). When one system is a qubit, we identify the structure of product ensembles that can be perfectly discriminated by LOSCC. We show these conditions fail for LOSQC and provide the smallest-sized example in which a gap between LOSCC and LOSQC exists. Finally, we prove an uncertainty relation that yields error bounds in LOSQC state discrimination and noise thresholds for quantum position verification.