Polygamy of Distributed Entanglement

Abstract

While quantum entanglement is known to be monogamous (i.e. shared entanglement is restricted in multi-partite settings), here we show that distributed entanglement (or the potential for entanglement) is by nature polygamous. By establishing the concept of one-way unlocalizable entanglement (UE) and investigating its properties, we provide a polygamy inequality of distributed entanglement in tripartite quantum systems of arbitrary dimension. We also provide a polygamy inequality in multi-qubit systems, and several trade offs between UE and other correlation measures.

9 pages, 1 figure, few typos corrected

References in corpus (16)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Distributed Entanglement
• Classical, quantum and total correlations
• Separability criterion and inseparable mixed states with positive partial transposition
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy of entanglement and other correlations
• Localizable Entanglement
• Is Entanglement Monogamous?
• Entanglement of assistance and multipartite state distillation
• Duality for monogamy of entanglement
• Distilling common randomness from bipartite quantum states
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Cited by in corpus (36)

• Tsallis entropy and entanglement constraints in multi-qubit systems
• Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation
• Quantum-memory-assisted entropic uncertainty relations
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• Limitations to sharing entanglement
• General polygamy inequality of multi-party quantum entanglement
• Why the Entanglement of Formation is not generally monogamic
• Bound of Entanglement of Assistance and Monogamy Constraints
• Weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems
• Demonstrating shareability of multipartite Einstein-Podolsky-Rosen steering
• Superactivation of monogamy relations for nonadditive quantum correlation measures
• Any entanglement of assistance is polygamous
• Tight Bounds on the Accessible Information and the Informational Power
• Accessible Information and Informational Power of Quantum 2-designs
• Unification of multi-qubit polygamy inequalities
• The one-way unlocalizable quantum discord
• Polygamy of Entanglement in Multipartite Quantum Systems
• Monogamy of quantum entanglement
• Tighter monogamy and polygamy relations of multiparty quantum entanglement
• Private quantum decoupling and secure disposal of information
• Tightening monogamy and polygamy relations of unified entanglement in multipartite systems
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Tighter constraints of multiqubit entanglement in terms of unified entropy
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Polygamy relations of multipartite systems
• Tighter monogamy and polygamy relations for a superposition of the generalized $W$-class state and vacuum
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Polygamy relations of multipartite entanglement beyond qubits
• Tighter constraints of multiqubit entanglement for negativity
• Polygamy of multi-party $q$-expected quantum entanglement
• Tighter weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems
• Strong polygamy of quantum correlations in multi-party quantum systems
• One-way Unlocalizable Information Deficit
• Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
• Multipartite distribution property of one way discord beyond measurement