Partial correlations in multipartite quantum systems.

Quantum correlations are more general than entanglement. A problem on how to characterize and quantify quantum correlations has attracted substantial attention. Quantum correlations in bipartite systems have been researched extensively. In this paper, partial correlations in a multipartite quantum system a 1 a 2 … a n are discussed in detail. In order to reveal correlations of a given state with respect to some subsystems, for a nonempty subset Δ of the index set { 1 , 2 , … , n } , Δ -classical correlations ( Δ -CC), Δ -quantum correlations ( Δ -QC), partially classical correlations (PCC) and genuinely quantum correlations (GQC) are introduced in a multipartite system. Subsequently, characterizations of Δ -CC are obtained. Secondly, a measure function G Δ ( ρ ) of partial correlations of a state ρ is defined and called the Δ -quantum discord. It is proved that G Δ ( ρ ) is nonnegative, independent of the choice of basis and invariant under local unitary transformations. It is also proved that a state ρ is Δ -CC if and only if G Δ ( ρ ) = 0 , and then it is Δ -QC if and only if G Δ ( ρ ) > 0 . Moreover, some relationships among partial correlations with respect to different Δ are discussed in light of the measure function. Finally, an illustrative example with 6-qubit GHZ state is given. [ABSTRACT FROM AUTHOR]