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Quantum capacity of thermal noise channel

Xiaoyu Chen

Published Feb 11, 2006• 0 citations
OpenAlex

Abstract

The quantum capacity of thermal noise channel (which is addressed as Gaussian quantum channel before) is studied, it turns out to be the maximum of the coherent information of a single use of the channel. The quantum capacity is achieved when the input state is a thermal noise state with infinitive energy. The capacity is achievable with quantum error-correction code. The quantum capacities of thermal noise channels with damping or amplification are also given. One of the most important issues of classical information theory is the Shannon formula, which is the capacity of an additive white Gaussian noise channel. It is achieved when the input is a Gaussian noise source with power constrain [1] [2]. C = log2 (1 + S), (1)

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•Aug 1, 2013•0 citations
The quantum capacity of thermal noise channel (which is addressed as Gaussian quantum channel before) is studied, it turns out to be the maximum of the coherent information of a single use of the channel. The quantum capacity is achieved when the input state is a thermal noise state with infinitive energy. The capacity is achievable with quantum error-correction code. The quantum capacities of thermal noise channels with damping or amplification are also given. One of the most important issues of classical information theory is the Shannon formula, which is the capacity of an additive white Gaussian noise channel. It is achieved when the input is a Gaussian noise source with power constrain [1] [2]. C = log2 (1 + S), (1)
For a quantum channel with additive Gaussian quantum noise, at the large input energy side, we prove that the one shot capacity is achieved by the thermal noise state for all Gaussian state inputs, it is also true for non-Gaussian input in the sense of first order perturbation. For a general case of nnn copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.
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.
For a quantum channel of additive Gaussian noise with loss, in the general case of nnn copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.
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 classical capacity of quantum channels is the tight upper bound for the transmission rate of classical information. This is a quantum counterpart of the foundational notion of the channel capacity introduced by Shannon. Bosonic Gaussian quantum channels provide a good model for optical communications. In order to properly define the classical capacity for these quantum systems, an energy constraint at the channel input is necessary, as in the classical case. A further restriction to Gaussian input ensembles defines the Gaussian (classical) capacity, which can be studied analytically. It also provides a lower bound on the classical capacity and moreover, it is conjectured to coincide with the classical capacity. Therefore, the Gaussian capacity is a useful and important notion in quantum information theory. Recently, we have shown that the study of both the classical and Gaussian capacity of an arbitrary single mode Gaussian quantum channel can be reduced to the study of a particular fiducial channel. In this work we consider the Gaussian capacity of the fiducial channel, discuss its additivity and analyze its dependence on the channel parameters. In addition, we extend previously obtained results on the optimal channel environment to the single mode fiducial channel. In particular, we show that the optimal channel environment for the lossy, amplification, and phase conjugating channels is given by a pure quantum state if its energy is constrained.