Local Simultaneous State Discrimination
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 the problem does not trivialize for classical states to a non-distributed distinguishing task.
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.
While interesting in its own right, this problem also arises in quantum cryptography. In particular, we explore the connections of the problem between unclonable encryption and LSSD. We give an explicit cloning-indistinguishable attack that succeeds with probability 1/2 + μ/16 where μ is related to the largest eigenvalue of the resulting quantum ciphertexts.
Joint work with Christian Majenz, Maris Ozols and Mehrdad Tahmasbi (https://arxiv.org/abs/2103.14510 and another article to appear on arxiv soon)
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