Classical communication with indefinite causal order for N completely depolarizing channels

Sk Sazim, Michal Sedlak, Kratveer Singh, and Arun Kumar Pati
Phys. Rev. A 103, 062610 – Published 16 June 2021

Abstract

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit nonzero classical information. Here we study how well we can transmit classical information with N depolarizing channels put in superposition of M causal orders via a quantum switch. We calculate the Holevo quantity if the superposition uses only cyclic permutations of channels and find that it increases with M and it is independent of N. For a qubit it never reaches 1 if we are increasing M. On the other hand, the classical capacity decreases with the dimension d of the message system. Further, for N=3 and 4 we studied the superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by a cyclic permutation subgroup.

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  • Received 28 April 2021
  • Accepted 2 June 2021

DOI:https://doi.org/10.1103/PhysRevA.103.062610

©2021 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Sk Sazim1,*, Michal Sedlak1,†, Kratveer Singh2, and Arun Kumar Pati3

  • 1RCQI, Institute of Physics, Slovak Academy of Sciences, 845 11 Bratislava, Slovakia
  • 2Indian Institute of Science Education and Research, Bypass Road, Bhauri, Bhopal 462066, India
  • 3QIC Group, Harish-Chandra Research Institute, Homi Bhabha National Institute, Allahabad 211019, India

  • *sk.sazimsq49@gmail.com
  • michal.sedlak@savba.sk

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Vol. 103, Iss. 6 — June 2021

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