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

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.

Quantum correlations as precursors of entanglement

“…Although Ω 12 diverges in this limit, Eq. (19) shows that the evolution of the initial quantum state considered here is independent of the dipole-dipole interaction. Therefore, in this limit we do recover, for the considered initial state, the evolution predicted by the Dicke model.…”

“…The density matrix for this model is easily obtained from Eqs. (18) and (19) taking the limit γ → 1:…”

“…(19) and from the inequality cosh(γτ ) − e −τ > sinh(γτ ) that b(τ ) > 0 for all τ . Therefore, the concurrence is zero in this case.…”

“…The MID presents a great advantage with respect to the quantum discord: it is easily calculable, since it does not involve any minimization, one has only to find the eigenvectors of the density matrices corresponding to the subsystems. However, it is not applicable in all cases as Wu et al [19] have remarked: when the local density matrices have degenerate eigenvalues, the MID is not uniquely defined.…”

“…(19) and α = [2(a(τ ) + b(τ )) − 1] 2 + 4|c(τ )| 2 . Figure 6 displays the classical correlations and the concurrence for several values of the parameter γ.…”