Abstract
We consider online strategies for discriminating between symmetric pure states with zero error when n copies of the states are provided. Optimized online strategies involve local, possibly adaptive measurements on each copy and are optimal at each step, which makes them robust in front of particle losses or an abrupt termination of the discrimination process. We first review previous results on binary minimum and zero error discrimination with local measurements that achieve the maximum success probability set by optimizing over global measurements, highlighting their online features. We then extend these results to the case of zero error identification of three symmetric states with constant overlap. We provide optimal online schemes that attain global performance for any n if the state overlaps are positive, and for odd n if overlaps have a negative value. For arbitrary complex overlaps, we show compelling evidence that online schemes fail to reach optimal global performance. The online schemes that we describe only require to store the last outcome obtained in a classical memory, and adaptiveness of the measurements reduce to at most two changes, regardless of the value of n.
Highlights
The task of discriminating among nonorthogonal quantum states [1–4] underlies many prominent applications of quantum information sciences
Once optimized, is guaranteed to yield the best performance in the discrimination task allowed by quantum mechanics, but the necessary requirements to implement it are hardly met in practical situations
We show that the optimal performance given by Eq (11) can always be attained with local measurements
Summary
The task of discriminating among nonorthogonal quantum states [1–4] underlies many prominent applications of quantum information sciences. The question of when can LOCC schemes attain optimal (global) performance in a state discrimination task has been considered in the literature under different angles [17–26]. We tackle the problem of unambiguous (zero error) identification of three symmetric pure quantum states with constant (but arbitrary) overlap c when n copies are provided, characterizing for which parameter ranges do online schemes attain global performance. This serves us to set notation and techniques that we use later.
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