Sequential State Discrimination and Requirement of Quantum Dissonance

TL;DR

This paper investigates sequential unambiguous state discrimination of a qubit, revealing that quantum discord, rather than entanglement, is essential for the process and optimizing the probability of successful discrimination.

Contribution

It demonstrates that quantum dissonance is necessary for sequential state discrimination and identifies the conditions under which the probability of successful identification is maximized.

Findings

Quantum discord is essential for unambiguous state discrimination.

Maximum success probability occurs when the product of left and right discord is maximized.

Entanglement is not required for the discrimination process.

Abstract

We study the procedure for sequential unambiguous state discrimination. A qubit is prepared in one of two possible states, and measured by two observers Bob and Charlie sequentially. A necessary condition for the state to be unambiguously discriminated by Charlie is the absence of entanglement between the principal qubit, prepared by Alice, and Bob's auxiliary system. In general, the procedure for both Bob and Charlie to recognize between two nonorthogonal states conclusively relies on the availability of quantum discord which is precisely the quantum dissonance when the entanglement is absent. In Bob's measurement, the left discord is positively correlated with the information extracted by Bob, and the right discord enhances the information left to Charlie. When their product achieves its maximum the probability for both Bob and Charlie to identify the state achieves its optimal value.