Multiaccess quantum communication and product higher rank numerical range

  • Authors:

  • Maciej Demianowicz;Paweł Horodecki;Karol Zyczkowski

  • Affiliations:

  • Department of Atomic Physics and Luminescence, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gdansk, Poland and National Quantum Information Center in Gdansk, Sopot, ...;Department of Theoretical Physics and Quantum Informatics, Faculty of Applied Physics and Mathematics, Gdansk University of Technology, Gdansk, Poland and National Quantum Information Center in Gd ...;Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland and Center of Theoretical Physics, Polish Academy of Science, Warszawa, Poland

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2013

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Abstract

In the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range [M.-D. Choi et al., Rep. Math. Phys. 58, 77 (2006); Lin. Alg. Appl. 418, 828 (2006)], is a natural tool for studying a construction of quantum error correction codes for multiple access channels. We review properties of this set and relate it to other numerical ranges, which were recently introduced in the literature. Further, the concept is applied to the construction of codes for bi-unitary two-access channels with a hermitian noise model. Analytical techniques for both outerbounding the product higher rank numerical range and determining its exact shape are developed for this case. Finally, the reverse problem of constructing a noise model for a given product range is considered.