Entanglement of Collaboration

Abstract

The entanglement of collaboration (EoC) quantifies the maximum amount of entanglement, that can be generated between two parties, A and B, given collaboration with N-2 other parties, when the N parties share a multipartite (possibly mixed) state and where the collaboration consists of local operations and classical communication (LOCC) by all parties. The localizable entanglement (LE) is defined similarly except that A and B do not participate in the effort to generate bipartite entanglement. We compare between these two operational definitions and find sufficient conditions for which the EoC is equal to the LE. In particular, we find that the two are equal whenever they are measured by the concurrence or by one of its generalizations called the G-concurrence. We also find a simple expression for the LE in terms of the Jamiolkowski isomorphism and prove that it is convex.

6 pages, to appear in Phys. Rev. A

References in corpus (16)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• The logarithmic negativity: A full entanglement monotone that is not convex
• Universal state inversion and concurrence in arbitrary dimensions
• Entanglement monotones
• Quantum information can be negative
• Entanglement versus Correlations in Spin Systems
• Diverging Entanglement Length in Gapped Quantum Spin Systems
• Localizable Entanglement
• Three-spin interactions in optical lattices and criticality in cluster Hamiltonians
• Entanglement of assistance and multipartite state distillation
• Family of Concurrence Monotones and its Applications
• Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems
• Entanglement of Assistance is not a bipartite measure nor a tripartite monotone
• Mixed State Entanglement of Assistance and the Generalized Concurrence
• Transport of Entanglement Through a Heisenberg-XY Spin Chain

Cited by in corpus (12)

• Quantifying entanglement resources
• Recovering Entanglement by Local Operations
• Bound of Entanglement of Assistance and Monogamy Constraints
• Constructing monotones for quantum phase references in totally dephasing channels
• Entanglement of assistance in three-qubit systems
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Entanglement and its facets in condensed matter systems
• How many ebits can be unlocked with one classical bit?
• Manipulation of tripartite-to-bipartite entanglement localization under quantum noises and its application to entanglement distribution
• Entanglement of Assistance as a measure of multiparty entanglement
• Experimental demonstration of a fully inseparable quantum state with nonlocalizable entanglement
• Tripartite-to-bipartite Entanglement Transformation by Stochastic Local Operations and Classical Communication and the Structure of Matrix Spaces