Requirement of Dissonance in Assisted Optimal State Discrimination

TL;DR

This paper demonstrates that quantum dissonance, rather than entanglement, is essential for assisted optimal quantum state discrimination, highlighting the specific quantum correlations responsible for the process.

Contribution

It introduces a more general joint unitary transformation and shows dissonance's crucial role over entanglement in state discrimination.

Findings

Entanglement can be eliminated without affecting success probability.

Quantum dissonance is necessary for optimal state discrimination.

A criterion based on linear entropy for the necessity of dissonance is provided.

Abstract

A fundamental problem in quantum information is to explore what kind of quantum correlations is responsible for successful completion of a quantum information procedure. Here we study the roles of entanglement, discord, and dissonance needed for optimal quantum state discrimination when the latter is assisted with an auxiliary system. In such process, we present a more general joint unitary transformation than the existing results. The quantum entanglement between a principal qubit and an ancilla is found to be completely unnecessary, as it can be set to zero in the arbitrary case by adjusting the parameters in the general unitary without affecting the success probability. This result also shows that it is quantum dissonance that plays as a key role in assisted optimal state discrimination and not quantum entanglement. A necessary criterion for the necessity of quantum dissonance based on the linear entropy is also presented.