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 (25)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Introducing Quantum Discord
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• Universal state inversion and concurrence in arbitrary dimensions
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy of entanglement and other correlations
• "Squashed Entanglement" - An Additive Entanglement Measure
• Fidelity and Concurrence of conjugated states
• Measures and dynamics of entangled states
• Concurrence of mixed multi-partite quantum states
• Conservation law for distributed entanglement of formation and quantum discord
• Are general quantum correlations monogamous?
• Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations
• Violation of monogamy inequality for higher-dimensional objects
• 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
• Why the Entanglement of Formation is not generally monogamic
• Strong superadditivity and monogamy of the Renyi measure of entanglement
• Efficient numerical method to calculate three-tangle of mixed states
• Classification of Tripartite Entanglement with one Qubit

Cited by in corpus (24)

• Monogamy of quantum correlations - a review
• Monogamy of entanglement of formation
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Should Entanglement Measures be Monogamous or Faithful?
• Monogamy of entanglement without inequalities
• General monogamy relation of multi-qubit systems in terms of squared Rényi-$\alpha$ entanglement
• Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Strong monogamy inequalities for four qubits
• Monogamy relation of multi-qubit systems for squared Tsallis-\emph{q} entanglement
• Entangled Datasets for Quantum Machine Learning
• On Strong Monogamy Conjecture in Four-Qubit System
• Monogamy of quantum entanglement
• Lower bounds on violation of monogamy inequality for quantum correlation measures
• Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• Multi-linear Monogamy Relations for Three Qubit States
• Multipartite Monogamy of Entanglement for Three Qubit States
• Entanglement of Assistance as a measure of multiparty entanglement
• Classification of three-qubit genuine entangled states using concurrence fill
• Strain induced coupling and quantum information processing with hexagonal boron nitride quantum emitters
• Distributed entanglement generation from asynchronously excited qubits