Multipartite monogamy of the concurrence

Abstract

Monogamy of entanglement is generally discussed using a bipartite entanglement measure as an upper bound. Here we discuss a new kind of monogamous relation where the upper bound is given by a multipartite measure of entanglement, the generalized concurrence. We show a new monogamous equality involving the multipartite concurrence, all the bipartite concurrences and the genuine tripartite entanglement for pure three qubits system. The result extends to mixed states in an inequality involving the generalized concurrence and all the bipartite concurrences. We provide a counter-example showing that the result cannot be extended for systems with more than three qubits.

4 pages

References in corpus (7)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Conservation law for distributed entanglement of formation and quantum discord
• Entanglement irreversibility from quantum discord and quantum deficit
• Three-tangle for mixtures of generalized GHZ and generalized W states
• Monogamy of Bell's inequality violations in non-signaling theories
• Strong Monogamy of Bipartite and Genuine Multipartite Entanglement: The Gaussian Case
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states