Tripartite genuinely entangled states from entanglement-breaking subspaces
arXiv:2006.05128 · doi:10.1088/1751-8121/abce20
Abstract
The determination of genuine entanglement is a central problem in quantum information processing. We investigate the tripartite state as the tensor product of two bipartite entangled states by merging two systems. We show that the tripartite state is a genuinely entangled state when the range of both bipartite states are entanglement-breaking subspaces. We further investigate the tripartite state when one of the two bipartite states has rank two. Our results provide the latest progress on a conjecture proposed in the paper [Yi Shen , J. Phys. A 53, 125302 (2020)]. We apply our results to construct multipartite states whose bipartite reduced density operators have additive EOF. Further, such states are distillable across every bipartition under local operations and classical communications.
References in corpus (46)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- Three qubits can be entangled in two inequivalent ways
- Distributed Entanglement
- Measurement-based quantum computation
- Multipartite entanglement for continuous variables: A quantum teleportation network
- Quantum Phase Transitions and Bipartite Entanglement
- Entanglement Measures under Symmetry
- The asymptotic entanglement cost of preparing a quantum state
- Taming multiparticle entanglement
- Entanglement of formation for symmetric Gaussian states
- Measure of genuine multipartite entanglement with computable lower bounds
- Separability and distillability of multiparticle quantum systems
- Device-independent witnesses of genuine multipartite entanglement
- Detection of high-dimensional genuine multi-partite entanglement of mixed states
- The Entanglement of Formation for Isotropic States
- Evidence for Bound Entangled States with Negative Partial Transpose
- Distillability and partial transposition in bipartite systems
- Genuine quantum nonlocality in the triangle network
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Multipartite Entanglement Witnesses
- Entanglement of Formation of Bipartite Quantum States
- Entanglement cost of mixed states
- Multipartite entanglement detection from correlation tensors
- Witnessing genuine multipartite entanglement with positive maps
- The entropy vector formalism and the structure of multidimensional entanglement in multipartite systems
- On the permutationally invariant part of a density matrix and nonseparability of N-qubit states
- Measure of multipartite entanglement with computable lower bounds
- Relaxations of separability in multipartite systems: Semidefinite programs, witnesses and volumes
- Improved lower bounds on genuine-multipartite-entanglement concurrence
- Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
- Additivity and non-additivity of multipartite entanglement measures
- Generalized concurrence measure for faithful quantification of multiparticle pure state entanglement using Lagrange's identity and wedge product
- Study of the Distillability of Werner States Using Entanglement Witnesses and Robust Semidefinite Programs
- Genuine Multipartite Entanglement in the Cluster-Ising Model
- Characterization of Distillable and Activable States using Entanglement Witnesses
- Multi-copy and stochastic transformation of multipartite pure states
- Disentanglement Cost of Quantum States
- Quantum Advantage in Communication Networks
- Multipartite quantum correlations in even and odd spin coherent states
- Improved entanglement detection with subspace witnesses
- Construction of genuine multipartite entangled states
- On two-distillable Werner states
- Additivity of entanglement of formation via entanglement-breaking space
- Non-distillable entanglement guarantees distillable entanglement