Monogamy of the Entanglement of Formation

Abstract

We show that any measure of entanglement that on pure bipartite states is given by a strictly concave function of the reduced density matrix is monogamous on pure tripartite states. This includes the important class of bipartite measures of entanglement that reduce to the (von Neumann) entropy of entanglement. Moreover, we show that the convex roof extension of such measures (e.g., entanglement of formation) are monogamous also on \emph{mixed} tripartite states. To prove our results, we use the definition of monogamy without inequalities, recently put forward[Gour and Guo, Quantum \textbf{2}, 81 (2018)]. Our results promote the theme that monogamy of entanglement is a property of quantum entanglement and not an attribute of some particular measures of entanglement.

7 pages, the title is changed, and a gap in the proof is fixed

References in corpus (15)

• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy Inequality in terms of Negativity for Three-Qubit States
• Is Entanglement Monogamous?
• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Entanglement monogamy relations of qubit systems
• Monogamy of quantum correlations - a review
• Demonstration of monogamy relations for Einstein-Podolsky-Rosen steering in Gaussian cluster states
• Duality for monogamy of entanglement
• Monogamy of entanglement without inequalities
• Generalized W-Class State and its Monogamy Relation
• Anisotropic invariance and the distribution of quantum correlations
• Monogamy inequality for any local quantum resource and entanglement
• Entanglement sharing: from qubits to Gaussian states
• Any entanglement of assistance is polygamous
• Monogamy of particle statistics in tripartite systems simulating bosons and fermions

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• When is a Genuine Multipartite Entanglement Measure Monogamous?
• Complete monogamy of the multipartite quantum mutual information
• NSI effects on tripartite entanglement in neutrino oscillations
• On monogamy and polygamy relations of multipartite systems
• Monogamy of Entanglement Measures Based on Fidelity in Multiqubit Systems
• Monogamy of Logarithmic Negativity and Logarithmic Convex-Roof Extended Negativity
• An Extention of Entanglement Measures for Pure States
• Complete Genuine Multipartite Entanglement Monotone
• Trade-off relations of l_1-norm coherence for multipartite systems
• Partial-Norm of Entanglement: Entanglement Monotones That are not Monogamous
• Tighter monogamy relations in multiparty quantum systems
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Maximum Violation of Monogamy of Entanglement for Indistinguishable Particles by Measures that are Monogamous for Distinguishable Particles
• Parameterized bipartite entanglement measures and entanglement constraints
• Steering in Neutrino Oscillations with Non-Standard Interaction
• Features of preparable entangled states in Gaussian quantum networks
• Complete $k$-partite entanglement measure
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Unified monogamy relations for the generalized $W$-class states beyond qubits