Entangled graphs. II. Classical correlations in multiqubit entangled systems
Martin Plesch, Vladimír Bužek · Physical Review A · 2003
Bipartite correlations in multiqubit systems cannot be shared freely. The presence of entanglement or classical correlation on certain pairs of qubits may imply correlations on other pairs. We present a method of characterization of bipartite correlations in multiqubit systems using a concept of entangled graphs which has been introduced in our earlier work [M. Plesch and V. Bu\ifmmode \check{z}\else \v{z}\fi{}ek, Phys. Rev. A 67, 012322 (2003)]. In entangled graphs, each qubit is represented by a vertex while the entanglement and classical correlations are represented by two types of edges. We prove by construction that any entangled graph with classical correlations can be represented by a mixed state of N qubits. However, not all entangled graphs with classical correlations can be represented by a pure state.