Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
arXiv:2104.09664 · doi:10.1088/1751-8121/ac37e5
Abstract
Genuine entanglement is the strongest form of multipartite entanglement. Genuinely entangled pure states contain entanglement in every bipartition and as such can be regarded as a valuable resource in the protocols of quantum information processing. A recent direction of research is the construction of genuinely entangled subspaces -- the class of subspaces consisting entirely of genuinely multipartite entangled pure states. In this paper we present several methods of construction of such subspaces including those of maximal possible dimension. The approach is based on the correspondence between bipartite entangled subspaces and quantum channels of a certain type. The examples include maximal subspaces for systems of three qubits, four qubits, three qutrits. We also provide lower bounds on two entanglement measures for mixed states, the concurrence and the convex-roof extended negativity, which are directly connected with the projection on genuinely entangled subspaces.
arXiv comment17 pages, 6 figures. REVTEX
References in corpus (35)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Mixed State Entanglement and Quantum Error Correction
- A computable measure of entanglement
- Three qubits can be entangled in two inequivalent ways
- Distributed Entanglement
- Entanglement detection
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- Unextendible Product Bases and Bound Entanglement
- Four qubits can be entangled in nine different ways
- Monogamy of entanglement and other correlations
- Teleportation and Dense Coding with Genuine Multipartite Entanglement
- Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
- Perfect Teleportation, Quantum state sharing and Superdense Coding through a Genuinely Entangled Five-qubit State
- Computing quantum discord is NP-complete
- Separability and distillability of multiparticle quantum systems
- Monotones and invariants for multi-particle quantum states
- Is Entanglement Monogamous?
- Convex-roof extended negativity as an entanglement measure for bipartite quantum systems
- Counterexample to an additivity conjecture for output purity of quantum channels
- Entanglement cost of mixed states
- Contractivity of positive and trace preserving maps under norms
- On the dimension of subspaces with bounded Schmidt rank
- A completely entangled subspace of maximal dimension
- Quantum Codes of Maximal Distance and Highly Entangled Subspaces
- Concurrence in arbitrary dimensions
- Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
- From unextendible product bases to genuinely entangled subspaces
- Experimentally accessible lower bounds for genuine multipartite entanglement and coherence measures
- Entanglement of Subspaces and Error Correcting Codes
- Multipartite entanglement outperforming bipartite entanglement under limited quantum system sizes
- Lectures on Quantum Tensor Networks
- Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results
- An approach to constructing genuinely entangled subspaces of maximal dimension
- Lower bounds on concurrence and negativity from a trace inequality
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- Frustration graph formalism for qudit observables