Unextendibility, uncompletability, and many-copy indistinguishable ensembles

• URL: http://arxiv.org/abs/2303.17507v2
• Date: Tue, 25 Feb 2025 16:59:48 GMT
• Title: Unextendibility, uncompletability, and many-copy indistinguishable ensembles
• Authors: Saronath Halder, Alexander Streltsov,
• Abstract summary: We show that the complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality.<n>We also report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing number of mixed states.
• Score: 49.1574468325115
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we explore the notions unextendible product basis and uncompletability for operators which remain positive under partial transpose. Then, we analyze their connections to the ensembles which are many-copy indistinguishable under local operations and classical communication (LOCC). We show that the orthogonal complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality. This subspace has one to one correspondence with the maximum dimensional subspace where there is no orthonormal product basis. Due to these, the proof of indistinguishability of a class of ensembles under LOCC in many-copy scenario becomes simpler. Furthermore, it is now clear that there are several many-copy indistinguishable ensembles which are different construction-wise. But if we consider the technique of proving their indistinguishability property under LOCC, then, for many of them it can be done using the general notion of unextendible product basis. Explicit construction of the product states, forming nUPBs is shown. Thereafter, we introduce the notion of positive partial transpose uncompletability to unify different many-copy indistinguishable ensembles. We also report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing number of mixed states.

Related papers

• Multipartite Embezzlement of Entanglement [44.99833362998488]
  Embezzlement of entanglement refers to the task of extracting entanglement from an entanglement resource via local operations and without communication. We show that finite-dimensional approximations of multipartite embezzling states form multipartite embezzling families. We discuss our results in the context of quantum field theory and quantum many-body physics.
  arXiv  Detail & Related papers  (2024-09-11T22:14:22Z)
• Implications of sparsity and high triangle density for graph representation learning [67.98498239263549]
  Recent work has shown that sparse graphs containing many triangles cannot be reproduced using a finite-dimensional representation of the nodes. Here, we show that such graphs can be reproduced using an infinite-dimensional inner product model, where the node representations lie on a low-dimensional manifold.
  arXiv  Detail & Related papers  (2022-10-27T09:15:15Z)
• Orthogonal product sets with strong quantum nonlocality on plane structure [0.0]
  We construct a strongly nonlocal OPS in $mathcalCd_Aotimes mathcalCd_C$ $(d_A,B,Cgeq 4)$ and generalize the structures of known OPSs to any possible three and four-partite systems. It is shown that the protocols without teleportation use less entanglement resources on average and these sets can always be discriminated locally with multiple copies of 2-qubit maximally entangled states.
  arXiv  Detail & Related papers  (2022-05-22T13:07:16Z)
• Proofs of network quantum nonlocality aided by machine learning [68.8204255655161]
  We show that the family of quantum triangle distributions of [DOI40103/PhysRevLett.123.140] did not admit triangle-local models in a larger range than the original proof. We produce a large collection of network Bell inequalities for the triangle scenario with binary outcomes, which are of independent interest.
  arXiv  Detail & Related papers  (2022-03-30T18:00:00Z)
• Non-standard entanglement structure of local unitary self-dual models as a saturated situation of repeatability in general probabilistic theories [61.12008553173672]
  We show the existence of infinite structures of quantum composite system such that it is self-dual with local unitary symmetry. We also show the existence of a structure of quantum composite system such that non-orthogonal states in the structure are perfectly distinguishable.
  arXiv  Detail & Related papers  (2021-11-29T23:37:58Z)
• Universal construction of genuinely entangled subspaces of any size [0.0]
  We construct subspaces supporting only genuinely multipartite entangled states of any permissible dimensionality. An immediate consequence of our result is the possibility of constructing in the general multiparty scenario genuinely multiparty entangled mixed states with ranks up to the maximal dimension of a genuinely entangled subspace.
  arXiv  Detail & Related papers  (2021-11-19T13:04:43Z)
• Multipartite spatial entanglement generated by concurrent nonlinear processes [91.3755431537592]
  Continuous variables multipartite entanglement is a key resource for quantum technologies. This work considers the multipartite entanglement generated in separated spatial modes of the same light beam by three different parametric sources.
  arXiv  Detail & Related papers  (2021-11-09T17:15:13Z)
• Capacity of Group-invariant Linear Readouts from Equivariant Representations: How Many Objects can be Linearly Classified Under All Possible Views? [21.06669693699965]
  We find that the fraction of separable dichotomies is determined by the dimension of the space that is fixed by the group action. We show how this relation extends to operations such as convolutions, element-wise nonlinearities, and global and local pooling.
  arXiv  Detail & Related papers  (2021-10-14T15:46:53Z)
• Separability and entanglement in superpositions of quantum states [0.0]
  We study the superpositions of a pure entangled state and a pure product state, when the amplitudes corresponding to the states appearing in any superposition are nonzero. All such superpositions produce only entangled states if the initial entangled state has Schmidt rank three or higher. We find that conditional inseparability of superpositions help in identifying strategies for conclusive local discrimination of shared quantum ensembles.
  arXiv  Detail & Related papers  (2021-08-04T19:48:29Z)
• Activation of genuine multipartite entanglement: Beyond the single-copy paradigm of entanglement characterisation [2.446672595462589]
  We show that multiple copies unlock genuine multipartite entanglement from partially separable states. We conjecture a strict hierarchy of activatable states and an collapse of the hierarchy.
  arXiv  Detail & Related papers  (2021-06-02T18:00:00Z)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)
• Unifying Two Notions of Nonlocality in Quantum Theory [0.0]
  We prove that a full product basis can create entangled states if and only if the full bases or any subspace of it become irreducible in the process of LOCC discrimination. For a set having entangled states, we modify the quantity accordingly and show that it can provide an explanation for the phenomena of more nonlocality with less entanglement.
  arXiv  Detail & Related papers  (2020-09-09T12:13:39Z)
• Local indistinguishability and incompleteness of entangled orthogonal bases: Method to generate two-element locally indistinguishable ensembles [0.0]
  Local indistinguishability of states with the properties of unextendibility and uncompletability of entangled bases for bipartite and multipartite quantum systems. We identify a method of constructing two-element ensembles, based on the concept of unextendible entangled bases, that can potentially lead to information sharing applications.
  arXiv  Detail & Related papers  (2020-08-04T15:04:27Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Nonlocal sets of orthogonal product states in arbitrary multipartite quantum system [0.0]
  We first give a simple method to construct a nonlocal set of product states in $otimes_j=1nmathbbCd$ for $dgeq 2$. Then we give an ingenious proof for local indistinguishability of the set constructed by our method. We generalize these two results to a more general $otimes_i=1nmathbbCd_j$ quantum system for $d_jgeq 2$.
  arXiv  Detail & Related papers  (2020-03-15T15:35:45Z)

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.