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Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups

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Abstract

In this paper we describe a class of highly entangled subspaces of a tensor product of finite-dimensional Hilbert spaces arising from the representation theory of free orthogonal quantum groups. We determine their largest singular values and obtain lower bounds for the minimum output entropy of the corresponding quantum channels. An application to the construction of d-positive maps on matrix algebras is also presented.

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Authors and Affiliations

  1. Department of Mathematics, Mailstop 3368, Texas A&M University, College Station, TX, 77843-3368, USA

    Michael Brannan

  2. Department of Mathematics, Kyoto University, Kyoto, Japan

    Benoît Collins

  3. CNRS, Institut Camille Jordan Université, Lyon 1, France

    Benoît Collins

Authors
  1. Michael Brannan
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  2. Benoît Collins
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Correspondence to Benoît Collins.

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Communicated by M. M. Wolf

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Brannan, M., Collins, B. Highly Entangled, Non-random Subspaces of Tensor Products from Quantum Groups. Commun. Math. Phys. 358, 1007–1025 (2018). https://doi.org/10.1007/s00220-017-3023-6

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  • DOI: https://doi.org/10.1007/s00220-017-3023-6

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