Classical Communications with Indefinite Causal Order for \(N\) completely depolarizing channels

If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with \(N\) depolarizing channels put in superposition of \(M\) ca...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Sazim, Sk, Sedlak, Michal, Singh, Kratveer, Pati, Arun Kumar
Format: Article
Language:English
Subjects:
Channels
Communication
Depolarization
Quantum mechanics
Qubits (quantum computing)
Online Access:Get full text
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Summary:If two identical copies of a completely depolarizing channel are put into a superposition of their possible causal orders, they can transmit non-zero classical information. Here, we study how well we can transmit classical information with \(N\) depolarizing channels put in superposition of \(M\) causal orders via quantum SWITCH. We calculate 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 \(N=4\) we studied superposition of all causal orders and uniformly superposed causal orders belonging to different cosets created by cyclic permutation subgroup.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.14339