Unextendible product bases, bound entangled states, and the range criterion

• URL: http://arxiv.org/abs/2005.02108v3
• Date: Mon, 1 Feb 2021 19:15:22 GMT
• Title: Unextendible product bases, bound entangled states, and the range criterion
• Authors: Pratapaditya Bej, Saronath Halder
• Abstract summary: We consider reducible and irreducible UPBs of maximum size, which can produce bound entangled (BE) states. We provide different UPBs corresponding to the present BE states of minimum rank and discuss important properties of the UPBs.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An unextendible product basis (UPB) is a set of orthogonal product states which span a subspace of a given Hilbert space while the complementary subspace contains no product state. These product bases are useful to produce bound entangled (BE) states. In this work we consider reducible and irreducible UPBs of maximum size, which can produce BE states of minimum rank. From a reducible UPB, it is possible to eliminate one or more states locally, keeping the post-measurement states orthogonal. On the other hand, for an irreducible UPB, the above is not possible. Particularly, the UPBs of the present size are important as they might be useful to produce BE states, having ranks of the widest variety, which satisfy the range criterion. Here we talk about such BE states. We also provide other types of BE states and analyze certain properties of the states. Some of the present BE states are associated with the tile structures. Furthermore, we provide different UPBs corresponding to the present BE states of minimum rank and discuss important properties of the UPBs.

Related papers

• Strong quantum nonlocality: Unextendible biseparability beyond unextendible product basis [0.0]
  An unextendible biseparable basis (UBB) is a set of pure biseparable states which span a subspace of a given space. We show that there exists a UBB which can demonstrate the phenomenon of strong quantum nonlocality.
  arXiv  Detail & Related papers  (2024-04-08T21:33:17Z)
• Embezzlement of entanglement, quantum fields, and the classification of von Neumann algebras [41.94295877935867]
  We study the quantum information theoretic task of embezzlement of entanglement in the setting of von Neumann algebras. We quantify the performance of a given resource state by the worst-case error. Our findings have implications for relativistic quantum field theory, where type III algebras naturally appear.
  arXiv  Detail & Related papers  (2024-01-14T14:22:54Z)
• Unextendibility, uncompletability, and many-copy indistinguishable ensembles [77.34726150561087]
  We study unextendibility, uncompletability and analyze their connections to many-copy indistinguishable ensembles. We report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing mixedness.
  arXiv  Detail & Related papers  (2023-03-30T16:16:41Z)
• Unextendible product bases from orthogonality graphs [24.740502616119606]
  Unextendible product bases play a key role in the study of quantum entanglement and nonlocality. We show that every minimal GUPB saturating our bound must be associated to regular graphs. We discuss a possible path towards the construction of a minimal GUPB in a tripartite system of minimal local dimension.
  arXiv  Detail & Related papers  (2023-03-05T02:33:22Z)
• Unextendible and uncompletable product bases in every bipartition [23.76183357793457]
  Unextendible product basis is an important object in quantum information theory. We find some unextendible product bases that are uncompletable product bases in every bipartition. Our results advance the understanding of the geometry of unextendible product bases.
  arXiv  Detail & Related papers  (2022-07-11T10:49:34Z)
• Small set of orthogonal product states with nonlocality [3.325625311163865]
  We study the locally stable set of product states with small size. It is well known that unextendible product basis (UPB) is locally indistinguishable. On the other hand, there exists some small subset of minimum size UPB that are also locally stable.
  arXiv  Detail & Related papers  (2022-07-11T03:44:15Z)
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases [0.0]
  Unextendible product bases (UPBs) provide a versatile tool with various applications across different areas of quantum information theory. An open question asks about the existence of UPBs, which are genuinely unextendible, i.e., they are not extendible even with biproduct vectors. We show that there are always forbidden cardinalities for such UPBs, including the minimal ones corresponding to GESs of the maximal dimensions.
  arXiv  Detail & Related papers  (2022-02-16T22:15:49Z)
• Machine-Learning-Derived Entanglement Witnesses [55.76279816849472]
  We show a correspondence between linear support vector machines (SVMs) and entanglement witnesses. We use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states.
  arXiv  Detail & Related papers  (2021-07-05T22:28:02Z)
• Strongly nonlocal unextendible product bases do exist [14.686974497801048]
  We show the existence of unextendible product bases (UPBs) that are locally irreducible. These UPBs exhibit the phenomenon of strong quantum nonlocality without entanglement. It sheds new light on the connections between UPBs and strong quantum nonlocality.
  arXiv  Detail & Related papers  (2021-01-04T01:51:52Z)
• Discrimination of quantum states under locality constraints in the many-copy setting [18.79968161594709]
  We prove that the optimal average error probability always decays exponentially in the number of copies. We show an infinite separation between the separable (SEP) and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB) On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is a UPB.
  arXiv  Detail & Related papers  (2020-11-25T23:26:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.