Assisted state discrimination without entanglement

TL;DR

This paper demonstrates that quantum discord, not entanglement, is essential for assisted optimal state discrimination, highlighting the role of quantum correlations beyond entanglement in quantum information tasks.

Contribution

It reveals that only one-sided quantum discord is needed for optimal assisted state discrimination and establishes conditions for zero discord in separable states.

Findings

Quantum discord is necessary for assisted state discrimination.

Only one-sided discord suffices for optimal discrimination.

PPT condition characterizes separability in certain states.

Abstract

It is shown that the dissonance, a quantum correlation which is equal to quantum discord for separable state, is required for assisted optimal state discrimination. We find that only one side discord is required in the optimal process of assisted state discrimination, while another side discord and entanglement is not necessary. We confirm that the quantum discord, which is asymmetric depending on local measurements, is a resource for assisted state discrimination. With the absence of entanglement, we give the necessary and sufficient condition for vanishing one side discord in assisted state discrimination for a class of $d$ nonorthogonal states. As a byproduct, we find that the positive-partial-transposition (PPT) condition is the necessary and sufficient condition for the separability of a class of $2\times d$ states.