Entangled graphs II: Classical correlations in multi-qubit entangled systems

Abstract

Bipartite correlations in multi-qubit 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 bi-partite correlations in multi-qubit systems using a concept of entangled graphs that has been introduced in our earlier work [M.Plesch and V.Buzek, 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.

7 pages, 4 figures, to appear in Phys. Rev. A

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• Separability Criterion for Density Matrices
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• Distributed Entanglement
• Entangled Rings
• Entangled webs: Tight bound for symmetric sharing of entanglement
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• Combinatorial Approaches in Quantum Information Theory