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Conference on Lasers and Electro-Optics

Quantum Channel Capacities

Jon Yard

Published Jan 1, 2012• 0 citations
Publisher

Abstract

Channel capacities measure the ultimate communication abilities of noisy channels. I discuss capacities for optical channels with Gaussian noise and show the capacity for quantum information has surprising aspects that could be probed experimentally.
DOI
10.1364/cleo_at.2012.jth1k.2

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The applications of the general formulae of channel capacity developed in the quantum information theory to evaluation of information transmission capacity of optical channel are interesting subjects. In this review paper, we will point out that the formulation based on only classical-quantum channel mapping model may be inadequate when one takes into account a power constraint for noisy channel. To define the power constraint well, we should explicitly consider how quantum states are conveyed through a transmission channel. Basing on such consideration, we calculate a capacity formula for an attenuated noisy optical channel with genreral Gaussian state input; this gives certain progress beyond the example in our former paper.
Communication over a noisy quantum channel introduces errors in the transmission that must be corrected. A fundamental bound on quantum error correction is the quantum capacity, which quantifies the amount of quantum data that can be protected. We show theoretically that two quantum channels, each with a transmission capacity of zero, can have a nonzero capacity when used together. This unveils a rich structure in the theory of quantum communications, implying that the quantum capacity does not completely specify a channel's ability to transmit quantum information.
We investigate the capacity of bosonic quantum channels for the transmission of quantum information. We calculate the quantum capacity for a class of Gaussian channels, including channels describing optical fibers with photon losses, by proving that Gaussian encodings are optimal. For arbitrary channels we show that achievable rates can be determined from few measurable parameters by proving that every channel can asymptotically simulate a Gaussian channel which is characterized by second moments of the initial channel. Along the way we provide a complete characterization of degradable Gaussian channels and those arising from teleportation protocols.
This paper defines a fundamentally new approach of capacity recovery of very noisy, practically completely useless optical quantum channels. The transmission of information through classical channels and quantum channels differs in many ways. The capacity recovery of very noisy communication channels cannot be imagined for classical systems, and this effect has no analogue in classical systems. The capacity recovery of very noisy quantum channels makes it possible to use two very noisy optical-fiber based quantum channels with a positive joint capacity at the output. Our method gives an algorithmic solution to the capacity recovery problem, and provides an efficient algorithmic solution for finding recoverable very noisy optical quantum channels.