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IEEE International Symposium on Information Theory (ISIT)

Quantum Gaussian channels

Alexander Semenovich Holevo, Osamu Hirota

Published Nov 7, 2002• 0 citations
Publisher

Abstract

The aim of this paper is explicit calculation of the classical capacity of quantum Gaussian channels, in particular, of those using squeezed states. The calculation is based on a general formula for the entropy of quantum Gaussian state, which is of independent interest, and on the recently proved coding theorem for quantum communication channels.

DOI
10.1109/isit.2000.866575

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The aim of this paper is explicit calculation of the classical capacity of quantum Gaussian channels, in particular, of those using squeezed states. The calculation is based on a general formula for the entropy of quantum Gaussian state, which is of independent interest, and on the recently proved coding theorem for quantum communication channels.
As its classical counterpart，quantum Gaussian noise is an important noise model in quantum information theory. The study of capacity of quantum Gaussian channel plays an important role in quantum communications. Based on the definition of quantum Gaussian state，the entropy of quantum Gaussian state，and Holevo bound theorem，the classical capacity of quantum Gaussian channel is given at first in the paper，where the classical capacity is defined as the capacity when only classical messages are transmitted through the quantum channel. Then，the classical capacities of quantum multiple access Gaussian channels are deduced according to the classical capacity theorem of multiple access quantum channels. For simplicity and generality，a multiple access quantum channel with two senders and one receiver is used for computation. The results can be generalized to the quantum channel with n senders and one receiver.
In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g., a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.
A long-standing problem on the classical capacity of bosonic Gaussian channels has recently been resolved by proving the minimum output entropy conjecture. It is also known that the ultimate capacity quantified by the Holevo bound can be achieved asymptotically by using an infinite number of channels. However, it is less understood to what extent the communication capacity can be reached if one uses a finite number of channels, which is a topic of practical importance. In this paper, we study the capacity of Gaussian communication, i.e., employing Gaussian states and Gaussian measurements to encode and decode information under a single-channel use. We prove that the optimal capacity of single-channel Gaussian communication is achieved by one of two well-known protocols, i.e., coherent-state communication or squeezed-state communication, depending on the energy (number of photons) as well as the characteristics of the channel. Our result suggests that the coherent-state scheme known to achieve the ultimate information-theoretic capacity is not a practically optimal scheme for the case of using a finite number of channels. We find that overall the squeezed-state communication is optimal in a small-photon-number regime whereas the coherent-state communication performs better in a large-photon-number regime.