Correlations in local measurements on a quantum state, and complementarity as an explanation of nonclassicality

TL;DR

This paper explores how quantum complementarity causes a gap between quantum and classical correlations in bipartite states, providing bounds and insights into nonclassicality and quantum computation.

Contribution

It introduces a quantitative analysis of the complementarity gap in correlations and relates it to classical correlation locking and quantum computational models.

Findings

Complementarity induces a measurable gap between quantum and classical correlations.

Upper bounds are derived for classical correlations in mutually unbiased bases.

The complementarity gap is observed in deterministic quantum computation with one qubit.

Abstract

We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how complementarity gives rise to a gap between the quantum and the classical correlations, and we relate our quantitative finding to the so-called classical correlation locked in a quantum state. We derive upper bounds for the sum of classical correlation obtained by measurements in different mutually unbiased bases and we show that the complementarity gap is also present in the deterministic quantum computation with one quantum bit.