Algorithmic complexity of quantum capacity

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Abstract

We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.

Keywords

Algorithmic complexity Quantum entropies Quantum channels Quantum capacity 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsIslamic Azad University, Varamin-Pishva BranchPishvaIran
  2. 2.School of Science and TechnologyUniversity of CamerinoCamerinoItaly
  3. 3.INFN–Sezione PerugiaPerugiaItaly

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