Deterministic Entanglement of Assistance and Monogamy Constraints

Abstract

Certain quantum information tasks require entanglement of assistance, namely a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that 'concurrence of assistance' (CoA) identifies capabilities and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that CoA is an entanglement monotone for $(2\times 2\times n)$-dimensional pure states. Moreover, if the CoA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.

5 pages, no figures

References in corpus (9)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Three qubits can be entangled in two inequivalent ways
• Distributed Entanglement
• Persistent entanglement in arrays of interacting particles
• Conditions for a class of entanglement transformations
• Entanglement monotones
• Local Distinguishability of Multipartite Orthogonal Quantum States
• Family of Concurrence Monotones and its Applications
• Remote Preparation and Distribution of Bipartite Entangled States

Cited by in corpus (70)

• Universal resources for measurement-based quantum computation
• 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
• Duality for monogamy of entanglement
• Fundamentals of universality in one-way quantum computation
• Entanglement Monogamy of Tripartite Quantum States
• Monogamy of entanglement without inequalities
• Generalized W-Class State and its Monogamy Relation
• Local Transformations Requiring Infinite Rounds of Classical Communication
• General polygamy inequality of multi-party quantum entanglement
• Entanglement of Assistance is not a bipartite measure nor a tripartite monotone
• Monogamy of quantum correlations in three qubit pure states using Rajagopal-Rendell (RR) quantum deficit
• Why the Entanglement of Formation is not generally monogamic
• Bound of Entanglement of Assistance and Monogamy Constraints
• Measurable entanglement for tripartite quantum pure states of qubits
• Multipartite Entanglement Accumulation in Quantum States: Localizable Generalized Geometric Measure
• Weighted polygamy inequalities of multiparty entanglement in arbitrary dimensional quantum systems
• Do Large Number of Parties Enforce Monogamy in All Quantum Correlations?
• Any entanglement of assistance is polygamous
• Robust tripartite-to-bipartite entanglement localization by weak measurements and reversal
• General Monogamy Relations of Quantum Entanglement for Multiqubit W-class States
• Complementary Quantum Correlations among Multipartite Systems
• Randomly distilling W-class states into general configurations of two-party entanglement
• The one-way unlocalizable quantum discord
• Monogamy of quantum entanglement
• Tripartite to Bipartite Entanglement Transformations and Polynomial Identity Testing
• Polygamy of Entanglement in Multipartite Quantum Systems
• Evolution equation for entanglement of assistance
• Tighter monogamy and polygamy relations of multiparty quantum entanglement
• Monogamy of entanglement for tripartite systems
• Heat transfer in transversely coupled qubits: Optically controlled thermal modulator with common reservoirs
• Concurrence of assistance and Mermin inequality on three-qubit pure states
• Tightening monogamy and polygamy relations of unified entanglement in multipartite systems
• Monogamy and entanglement in tripartite quantum states
• Monogamy equality in $2\otimes 2\otimes d$ quantum systems
• Monogamy relations of all quantum correlation measures for multipartite quantum systems
• Tighter constraints of multiqubit entanglement in terms of Rényi-$\alpha$ entropy
• On monogamy and polygamy relations of multipartite systems
• Polygamy relation for the Rényi-$\alpha$ entanglement of assistance in multi-qubit systems
• Entanglement of assistance in three-qubit systems
• Tighter monogamy and polygamy relations of quantum entanglement in multi-qubit systems
• Tighter constraints of multiqubit entanglement in terms of unified entropy
• Polygamy relations of multipartite systems
• Generation of entanglement via squeezing on a tripartite-optomechanical system
• Tighter monogamy and polygamy relations for a superposition of the generalized $W$-class state and vacuum
• Bounds on Bipartitiely Shared Entanglement Reduced from Superposed Tripartite Quantum States
• General Monogamy and polygamy properties of quantum systems
• Tighter generalized monogamy and polygamy relations for multiqubit systems
• Polygamy relations of multipartite entanglement beyond qubits
• Tighter constraints of multiqubit entanglement for negativity
• Tighter weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems
• Weighted monogamy and polygamy relations
• Strong polygamy of quantum correlations in multi-party quantum systems
• Polygamy relation of quantum correlations with equality
• A type of localized quadripartite entanglement
• Measurable genuine tripartite entanglement of ($2\otimes 2\otimes n$)-dimensional quantum states via only two simultaneous copies
• Fate of multiparticle entanglement when one particle becomes classical
• Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA
• Tighter Constraints of Multipartite Systems in terms of General Quantum Correlations
• Entanglement of Assistance as a measure of multiparty entanglement
• Superior monogamy and polygamy relations and estimates of concurrence
• Monogamy inequalities of entanglement of assistance in $2\otimes 2\otimes d$ systems
• Tighter bounds for generalized monogamy and polygamy relations
• Tripartite-to-bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces
• Monogamous nature of symmetric multiqubt states with distinct spinors
• Unified monogamy and polygamy relations for multipartite systems
• Tighter monogamy relations for the Tsallis-q and Rényi-$\alpha$ entanglement in multiqubit systems
• General monogamy and polygamy relations of arbitrary quantum correlations for multipartite systems
• Tighter monogamy and polygamy relations using Rényi-$\alpha$ entropy