Optimal discrimination of quantum sequences

TL;DR

This paper proves that for quantum sequence discrimination with independently and secretly drawn states, local measurements on individual states are sufficient to achieve optimal success, eliminating the need for collective measurements.

Contribution

It establishes that optimal discrimination of quantum sequences with independent states can be achieved through fixed local measurements, providing a clear criterion for measurement strategy.

Findings

Optimal success probability is achievable with local measurements.

No collective measurement is necessary for independent, secret sequences.

Applies to both minimum-error and unambiguous discrimination paradigms.

Abstract

A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely, quantum sequence discrimination, appears in various quantum information processing tasks, the objective being to determine the state of a finite sequence of quantum states. Since such a sequence is a composite quantum system, the fundamental question is whether an optimal measurement is local, i.e., comprising measurements on the individual members, or collective, i.e. requiring joint measurement(s). In some known instances of this problem, the optimal measurement is local, whereas in others, it is collective. But, so far, a definite prescription based solely on the problem description has been lacking. In this paper, we prove that if the members of a given sequence are drawn secretly and independently from an ensemble or even from different ensembles, the optimum success probability is achievable by fixed local measurements on the individual members of the sequence, and no collective measurement is necessary. This holds for both minimum-error and unambiguous state discrimination paradigms.