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arXiv:2010.02750 · Physics of Particles and Nuclei

Entropy Gain in ppp-Adic Quantum Channels

E. I. Zelenov

Published Jul 1, 2020• 8 citations
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Abstract

A configuration of a $$p$$ -adic quantum linear bosonic Gaussian channel is proposed. The entropy gain of such a channel is calculated. An adelic formula for the entropy gain is derived.

DOI
10.1134/s1063779620040814

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A configuration of a ppp -adic quantum linear bosonic Gaussian channel is proposed. The entropy gain of such a channel is calculated. An adelic formula for the entropy gain is derived.
In the present paper we study the entropy gain H(Φ[ρ])−H(ρ)H(Φ[ρ])-H(ρ)H(Φ[ρ])−H(ρ) for infinite-dimensional channels ΦΦΦ. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive \cite{al}, there is a plenty of channels with positive minimal entropy gain. We obtain the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states.
In the present paper we introduce and study Bosonic Gaussian classical-quantum (c-q) channels; the embedding of the classical input into quantum is always possible and therefore the classical entanglement-assisted capacity C_{ea} under appropriate input constraint is well defined. We prove a general property of entropy increase for weak complementary channel, that implies the equality C_{ea}=C (where C is the unassisted capacity) for certain class of c-q Gaussian channel under appropriate energy-type constraint. On the other hand, we show by explicit example that the inequality C