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Acta Sinica Quantum Optica

The Entanglement Assistant Capacity of Quantum Heat Noise Channel

Xiang-Jun Li

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

In this paper, we have studied the entanglement assistant capacity of single-mode heat noise channel with limited input power in which classical information is transmitted, and the same problem for those single-mode heat noise channels with amplifying and attenuating effects. For the heat noise channel, we have found that the capacity will be attained when input signal is heat noise and squeezed state is no useful for reaching the capacity. And for those single-mode heat noise channels with amplifying and attenuating effects the same result is obtained.

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In this paper, we have studied the entanglement assistant capacity of single-mode heat noise channel with limited input power in which classical information is transmitted, and the same problem for those single-mode heat noise channels with amplifying and attenuating effects. For the heat noise channel, we have found that the capacity will be attained when input signal is heat noise and squeezed state is no useful for reaching the capacity. And for those single-mode heat noise channels with amplifying and attenuating effects the same result is obtained.
There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian noises. We derive upper bounds the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.
There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian cases. We introduce new upper bounds on the energy-constrained quantum capacity of those channels by using the conditional quantum entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.
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.
We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel. If the environment state is thermal, we of course recover a Gaussian phase-covariant channel whose classical capacity is well known. Otherwise, we derive both a lower and an upper bound to the classical capacity of the channel, drawing inspiration from the classical treatment of the capacity of non-Gaussian additive-noise channels. We show that the lower bound to the capacity is always achievable and give examples where the non-Gaussianity of the channel can be exploited so that the communication rate beats the capacity of the Gaussian-equivalent channel (i.e. the channel where the environment state is replaced by a Gaussian state with the same covariance matrix). Finally, our upper bound leads us to formulate and investigate conjectures on the input state that minimizes the output entropy of non-Gaussian attenuator or amplifier channels. Solving these conjectures would be a main step toward accessing the capacity of a large class of non-Gaussian bosonic channels.