Duality for monogamy of entanglement

Abstract

We establish duality for monogamy of entanglement: whereas monogamy of entanglement inequalities provide an upper bound for bipartite sharability of entanglement in a multipartite system, we prove that the same quantity provides a \emph{lower} bound for distribution of bipartite entanglement in a multipartite system. Our theorem for monogamy of entanglement is used to establish relations between bipartite entanglement that separate one qubit from the rest vs separating two qubits from the rest.

12 pages

References in corpus (11)

• Entanglement of a Pair of Quantum Bits
• Classical, quantum and total correlations
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Monogamy of entanglement and other correlations
• Global entanglement in multiparticle systems
• Is Entanglement Monogamous?
• Distilling common randomness from bipartite quantum states
• Deterministic Entanglement of Assistance and Monogamy Constraints
• Remote Preparation and Distribution of Bipartite Entangled States
• Generalized decoding, effective channels, and simplified security proofs in quantum key distribution
• Bounds on general entropy measures

Cited by in corpus (78)

• Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity
• Entanglement monogamy relations of qubit systems
• Tsallis entropy and entanglement constraints in multi-qubit systems
• All Maximally Entangled Four Qubits States
• Unified entropy, entanglement measures and monogamy of multi-party entanglement
• Entanglement Monogamy of Tripartite Quantum States
• Monogamy of entanglement without inequalities
• Generalized W-Class State and its Monogamy Relation
• Polygamy of Distributed Entanglement
• Limitations to sharing entanglement
• Generalized Monogamy Relations of Concurrence for N-qubit Systems
• Monogamy of the Entanglement of Formation
• General polygamy inequality of multi-party quantum entanglement
• Bound of Entanglement of Assistance and Monogamy Constraints
• Weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems
• A new parameterized entanglement monotone
• Superactivation of monogamy relations for nonadditive quantum correlation measures
• Tighter constraints of multiqubit entanglement
• Possibility of generalized monogamy relations for multipartite entanglement beyond three qubits
• Any entanglement of assistance is polygamous
• Characterizing quantum states via sector lengths
• Exponentially many entanglement and correlation constraints for multipartite quantum states
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Finer Distribution of Quantum Correlations among Multiqubit Systems
• Quantum Correlation with Sandwiched Relative Entropies: Advantageous as Order Parameter in Quantum Phase Transitions
• Complementary Quantum Correlations among Multipartite Systems
• Unification of multi-qubit polygamy inequalities
• Parameterized Bipartite Entanglement Measure
• Monogamy of quantum entanglement
• Polygamy of Entanglement in Multipartite Quantum Systems
• Monogamy of entanglement for tripartite systems
• Tighter monogamy and polygamy relations of multiparty quantum entanglement
• Strict entanglement monotonicity under local operations and classical communication
• Tightening monogamy and polygamy relations of unified entanglement in multipartite systems
• Interference Visibility as a Witness of Entanglement and Quantum Correlation
• Lower bounds of concurrence for $N$-qubit systems and the detection of $k$-nonseparability of multipartite quantum systems
• Monogamy equality in $2\otimes 2\otimes d$ quantum systems
• Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• Realization of the tradeoff between internal and external entanglement
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Monogamy relations of concurrence for any dimensional quantum systems
• On monogamy and polygamy relations of multipartite systems
• Generalized Entanglement Monogamy and Polygamy Relations for N -Qubit Systems
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• 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
• General Monogamy and polygamy properties of quantum systems
• Tsallis entropy, $q$-expectation and constraints on three-party quantum correlations
• Numerical studies of entanglement properties in one- and two-dimensional quantum Ising and XXZ models
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Long range entanglement in quantum dot systems under the Fermi-Hubbard approach
• 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
• A new entanglement measure based on the total concurrence
• Persistency of Genuine Correlations Under Particle Loss
• Weighted monogamy and polygamy relations
• Strong polygamy and monogamy relations for multipartite quantum systems
• Strong polygamy of quantum correlations in multi-party quantum systems
• General monogamy relations of the $S^t$ and $T_q^t$-entropy entanglement measures based on dual entropy
• Polygamy Inequalities for Qubit Systems
• Parameterized bipartite entanglement measures and entanglement constraints
• Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
• Superior monogamy and polygamy relations and estimates of concurrence
• On two maximally entangled couples
• Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations
• Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy
• Monogamy and polygamy for multi-qudit generalized $W$-class states based on concurrence of assistance and Tsallis-$q$ entanglement of assistance
• Tighter bounds for generalized monogamy and polygamy relations
• Monogamous nature of symmetric multiqubt states with distinct spinors
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Unified monogamy relation of entanglement measures
• Unified monogamy and polygamy relations for multipartite systems
• Multiqubit monogamy relations beyond shadow inequalities
• General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems