Necessary and Sufficient Condition for Nonzero Quantum Discord

TLDR

Quantum discord characterizes nonclassical correlations in quantum mechanics and is considered a key resource in certain quantum communication tasks and computational models that exhibit little entanglement. Based on this, we propose a geometrical way of quantifying quantum discord. We introduce a geometrical method to quantify quantum discord, applying it to two‑qubit states and to the deterministic quantum computation with one qubit model. We derive a necessary and sufficient condition for nonzero quantum discord that is experimentally implementable, provide a closed‑form expression for two qubits, and show that discord is unlikely to explain the speedup in deterministic quantum computation with one qubit.

Abstract

Quantum discord characterizes ``nonclassicality'' 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 nonzero 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.