Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
arXiv:1809.04202 · doi:10.1103/PhysRevA.99.032335
Abstract
In a multipartite scenario quantum entanglement manifests its most dramatic form when the state is genuinely entangled. Such a state is more beneficial for information theoretic applications if it contains distillable entanglement in every bipartition. It is, therefore, of significant operational interest to identify subspaces of multipartite quantum systems that contain such properties apriori. In this letter, we introduce the notion of unextendible biseparable bases (UBB) that provides an adequate method to construct genuinely entangled subspaces (GES). We provide an explicit construction of two types of UBBs -- party symmetric and party asymmetric -- for every -{\it qudit} quantum system, with local dimension d\ge 3. Further, we show that the GES resulting from the symmetric construction is indeed a {\it bidistillable} subspace, i.e., all the states supported on it contain distillable entanglement across every bipartition.
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References in corpus (33)
- Quantum entanglement
- Three qubits can be entangled in two inequivalent ways
- Quantum secret sharing
- Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
- Entanglement detection
- Separability criterion and inseparable mixed states with positive partial transposition
- Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
- Quantum Nonlocality without Entanglement
- A quantum network of clocks
- Unextendible Product Bases and Bound Entanglement
- Aspects of generic entanglement
- Unextendible Product Bases, Uncompletable Product Bases and Bound Entanglement
- Multipartite Nonlocality without Entanglement in Many Dimensions
- Evidence for Bound Entangled States with Negative Partial Transpose
- Distillability and partial transposition in bipartite systems
- Strong Quantum Nonlocality without Entanglement
- Entanglement and permutational symmetry
- Modular architectures for quantum networks
- Witnessing genuine multipartite entanglement with positive maps
- A framework for bounding nonlocality of state discrimination
- On the dimension of subspaces with bounded Schmidt rank
- Generic local distinguishability and completely entangled subspaces
- The Minimum Size of Unextendible Product Bases in the Bipartite Case (and Some Multipartite Cases)
- Class of PPT bound entangled states associated to almost any set of pure entangled states
- The Structure of Qubit Unextendible Product Bases
- From unextendible product bases to genuinely entangled subspaces
- Non-Positive Partial Transpose Subspaces Can be as Large as Any Entangled Subspace
- Facial structures for various notions of positivity and applications to the theory of entanglement
- Non-positive-partial-transpose quantum states of rank four are distillable
- Optimal decomposable witnesses without the spanning property
- Statistical mechanics of multipartite entanglement
- Entanglement and decoherence: fragile and robust entanglement
- Entanglement properties of quantum grid states
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- Strong quantum nonlocality with entanglement
- Family of bound entangled states on the boundary of Peres set
- Strongly nonlocal unextendible product bases do exist
- Thermodynamic Signatures of Genuinely Multipartite Entanglement
- Multiparty orthogonal product states with minimal genuine nonlocality
- Strong quantum nonlocality for unextendible product bases in heterogeneous systems
- Multi-copy adaptive local discrimination: Strongest possible two-qubit nonlocal bases
- Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results
- Universal construction of genuinely entangled subspaces of any size
- An approach to constructing genuinely entangled subspaces of maximal dimension
- Activating Strongest Possible Nonlocality from Local Sets: An Elimination Paradigm
- Strong quantum nonlocality and unextendibility without entanglement in -partite systems with odd
- Unextendible and uncompletable product bases in every bipartition
- Simple sufficient condition for subspace to be completely or genuinely entangled
- Construction of genuinely multipartite entangled subspaces and the associated bounds on entanglement measures for mixed states
- Local Quantum State Marking
- Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis
- Fully non-positive-partial-transpose genuinely entangled subspaces
- A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
- Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
- Negative result about the construction of genuinely entangled subspaces from unextendible product bases
- Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles
- Tripartite genuinely entangled states from entanglement-breaking subspaces
- Quantifying subspace entanglement with geometric measures
- Strong nonlocal sets of UPB
- Unextendible and strongly uncompletable product bases
- On the state space structure of tripartite quantum systems
- Performance Analysis of Quantum CSS Error-Correcting Codes via MacWilliams Identities
- Entangled Subspaces through Algebraic Geometry
- Genuinely entangled subspaces beyond strongly nonlocal unextendible biseparable bases
- Entanglement of Assistance as a measure of multiparty entanglement
- Wigner's approach enabled detection of multipartite nonlocality using all different bipartitions
- Conclusive Local State Marking: More Nonlocality With No Entanglement
- Progress in the study of the (non)existence of genuinely unextendible product bases