Necessary and sufficient condition for non-zero quantum discord

TL;DR

This paper provides a complete criterion for when bipartite quantum states have non-zero quantum discord, introduces a geometric measure, and applies it to quantum computational models to analyze their speedup.

Contribution

It establishes a necessary and sufficient condition for non-zero quantum discord in bipartite states and proposes an experimentally feasible geometric quantification method.

Findings

Derived a simple criterion for non-zero quantum discord.

Obtained a closed-form expression for quantum discord in two-qubit systems.

Showed quantum discord is unlikely responsible for quantum speedup in certain models.

Abstract

Quantum discord characterizes "non-classicality" of correlations in quantum mechanics. It has been proposed as the key resource present in certain quantum communication tasks and quantum computational models without containing much entanglement. We obtain a necessary and sufficient condition for the existence of non-zero quantum discord for any dimensional bipartite states. This condition is easily experimentally implementable. Based on this, we propose a geometrical way of quantifying quantum discord. For two qubits this results in a closed form of expression for discord. We apply our results to the model of deterministic quantum computation with one qubit, showing that quantum discord is unlikely to be the reason behind its speedup.