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arXiv:1101.0264 · Physical Review A

Subadditivity of the minimum output entropy and superactivation of the classical capacity of quantum multiple access channels

Łukasz Czekaj

Published Apr 7, 2011• 6 citations
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Abstract

We study subadditivity of the minimum output entropy (${H}_{\text{min}}$) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for ${H}_{\text{min}}$ known in classical information theory. Our result is based on a fundamental property of $\text{MACs}$, i.e., independence of each sender. The channels used in the example can be constructed explicitly. On the basis of subadditivity of ${H}_{\text{min}}$ we also provide an example of extremal superadditivity (superactivation) of the classical capacity region of MACs.

DOI
10.1103/physreva.83.042304

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We study subadditivity of the minimum output entropy (Hmin{H}_{\text{min}}Hmin​) of quantum multiple access channels (MACs). We provide an example of violation of the additivity theorem for Hmin{H}_{\text{min}}Hmin​ known in classical information theory. Our result is based on a fundamental property of MACs\text{MACs}MACs, i.e., independence of each sender. The channels used in the example can be constructed explicitly. On the basis of subadditivity of Hmin{H}_{\text{min}}Hmin​ we also provide an example of extremal superadditivity (superactivation) of the classical capacity region of MACs.
We study classical capacity regions of quantum Gaussian multiple access channels (MAC). In classical variants of such channels, whilst some capacity superadditivity-type effects such as the so called water filling effect may be achieved, a fundamental classical additivity law can still be identified, viz. adding resources to one sender is never advantageous to other senders in sending their respective information to the receiver. Here, we show that quantum resources allow violation of this law, by providing an illustrative scheme of an experimentally feasible Gaussian MAC.
We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur. One of the more important open questions of quantum information theory is the determination of the capacity of a quantum channel for carrying classical information. This question has been only partially resolved. If entanglement between multiple inputs to the channel is not allowed, a formula for the classical capacity of a quantum channel has indeed been discovered [1, 2]. This capacity formula for a quantum channel Ψ is χ ∗ (Ψ) = max p i,ρ i H Ψ(piρi) − ∑