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Frontiers in Optics

Perfect Quantum Communication with Very Noisy Gaussian Optical Fiber Channels

László Gyöngyösi, Sándor Imre

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We demonstrate that very noisy Gaussian optical fiber quantum channels with zero zero-error capacities can be used to transmit information perfectly. We derive how the supremum of the superactivated capacity depends on the input states.
DOI
10.1364/fio.2011.fwy4

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We describe two quantum channels that individually cannot send any classical information without some chance of decoding error. But together a single use of each channel can send quantum information perfectly reliably. This proves that the zero-error classical capacity exhibits superactivation, the extreme form of the superadditivity phenomenon in which entangled inputs allow communication over zero-capacity channels. But our result is stronger still, as it even allows zero-error quantum communication when the two channels are combined. Thus our result shows a new remarkable way in which entanglement across two systems can be used to resist noise, in this case perfectly. We also show a new form of superactivation by entanglement shared between sender and receiver.
This paper introduces a fundamentally new method of finding the conditions for the superactivation of the zero-error capacity of quantum channels.The zero-error capacity of the quantum channel describes the amount of information which can be transmitted perfectly through a noisy quantum channel.The superactivation of the zero-error capacity of quantum channels makes it possible to use two quantum channels, each with zero zero-error capacity, with a positive joint zero-error capacity.Currently we have no theoretical background for describing all possible combinations of superactive quantum channels, hence there should be many other possible combinations.We give an algorithmic solution to the problem.To analyze the superactivation of the zero-error capacity, we introduce a new geometrical representation, called the quantum superball.Our method can be the first efficient algorithmic solution to discover the still unknown combinations to determine the superactivation of the zero-error capacity of quantum channels, without the extremely high computational costs.
The zero-error classical capacity of a quantum channel is the asymptotic rate at which it can be used to send classical bits perfectly, so that they can be decoded with zero probability of error. The study of zero-error capacities dates right back to Shannon and the early days of information theory. We show that there exist pairs of quantum channels, neither of which individually have any zero-error capacity whatsoever (even if arbitrarily many uses of the channels are available), but such that access to even a single copy of both channels allows classical information to be sent perfectly reliably. In other words, we prove that the zero-error classical capacity can be superactivated. This result is the first example of superactivation of a classical capacity of a quantum channel. We further strengthen this result to show that there exist pairs of channels, neither of which have any zero-error classical capacity (as before), yet for which access to one copy of the joint channel even allows far more delicate quantum information to be transmitted perfectly. This subsumes the first result, and also implies that the quantum zero-error capacity can be superactivated. But it is strictly stronger than either of these. Indeed, this is the strongest conceivable form of superactivation, and nothing similar is possible for standard Shannon capacities of quantum channels or for zero-error capacities of classical channels.