Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels

Abstract

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.

16pages, 8figures, and 2tables. Thoroughly revised with a major revision in Section.IV. A new Author has been added. Comments are welcome

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• Practical computational advantage from the quantum switch on a generalized family of promise problems
• Experimental Communication Through Superposition of Quantum Channels
• Interplay between the Hilbert-space dimension of a control system and the memory induced by a quantum SWITCH
• Indefinite Time Directed Quantum Metrology
• How Deep the Theory of Quantum Communications Goes: Superadditivity, Superactivation and Causal Activation
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• Sequential device-independent certification of indefinite causal order
• Entropic uncertainty under indefinite causal order and input-output direction
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