Information Capacity of a Communications Channel in the Presence of Quantum Effects

Alexander Semenovich Holevo

Cosmo Lupo, Vittorio Giovannetti, Stefano Pirandola +2 more

A wide variety of communication channels employ the quantized electromagnetic field to convey information. Their communication capacity crucially depends on losses associated to spatial characteristics of the channel such as diffraction and antenna design. Here we focus on the communication via a finite pupil, showing that diffraction is formally described as a memory channel. By exploiting this equivalence we then compute the communication capacity of an optical refocusing system, modeled as a converging lens. Even though loss of information originates from the finite pupil of the lens, we show that the presence of the refocusing system can substantially enhance the communication capacity. We mainly concentrate on communication of classical information, the extension to quantum information being straightforward.

Rouslan L. Stratonovich

C. H. Bennett, Peter W. Shor, John A. Smolin +1 more

The entanglement-assisted classical capacity of a noisy quantum channel (C/sub E/) is the amount of information per channel use that can be sent over the channel in the limit of many uses of the channel, assuming that the sender and receiver have access to the resource of shared quantum entanglement, which may be used up by the communication protocol. We show that the capacity C/sub E/ is given by an expression parallel to that for the capacity of a purely classical channel: i.e., the maximum, over channel inputs /spl rho/, of the entropy of the channel input plus the entropy of the channel output minus their joint entropy, the latter being defined as the entropy of an entangled purification of /spl rho/ after half of it has passed through the channel. We calculate entanglement-assisted capacities for two interesting quantum channels, the qubit amplitude damping channel and the bosonic channel with amplification/attenuation and Gaussian noise. We discuss how many independent parameters are required to completely characterize the asymptotic behavior of a general quantum channel, alone or in the presence of ancillary resources such as prior entanglement. In the classical analog of entanglement-assisted communication - communication over a discrete memoryless channel (DMC) between parties who share prior random information - we show that one parameter is sufficient, i.e., that in the presence of prior shared random information, all DMCs of equal capacity can simulate one another with unit asymptotic efficiency.

Hassan ZivariFard, Matthieu R. Bloch, Aria Nosratinia

We consider the problem of covert communication when Channel State Information (CSI) is available non-causally, causally, and strictly causally at both transmitter and receiver, as well as the case when channel state information is only available at the transmitter. Covert communication with respect to an adversary referred to as the "warden", is one in which the distribution induced during communication at the channel output observed by the warden is identical to the output distribution conditioned on an innocent channel-input symbol. In contrast to previous work, we do not assume the availability of a shared key at the transmitter and legitimate receiver; instead shared randomness is extracted from the channel state, in a manner that keeps it secret from the warden despite the influence of the channel state on the warden's output. When CSI is available at both transmitter and receiver, we derive the covert capacity region; when CSI is only available at the transmitter, we derive inner and outer bounds on the covert capacity. We also derive the covert capacity when the warden's channel is less noisy with respect to the legitimate receiver. We provide examples for which covert capacity is zero without channel state information, but is positive in the presence of channel state information.

Rouslan L. Stratonovich