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IEEE Transactions on Information Theory

Nonclassical states in optical communication to a remote receiver (Corresp.)

Carl W. Helstrom

Published May 1, 1980• 12 citations
Publisher

Abstract

The relation between the density operators of the aperture fields of a single-mode optical transmitter and a single-mode receiver is simply expressed in terms of their quasiprobability distributions. This formulation indicates that when the receiver is so far away that it picks up only a small fraction of the transmitted energy, the state induced in its aperture field by a nonclassical transmitted state differs only slightly from what it would be were a certain equivalent classical state transmitted instead. The implications for remote communications are discussed.

DOI
10.1109/tit.1980.1056176

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The relation between the density operators of the aperture fields of a single-mode optical transmitter and a single-mode receiver is simply expressed in terms of their quasiprobability distributions. This formulation indicates that when the receiver is so far away that it picks up only a small fraction of the transmitted energy, the state induced in its aperture field by a nonclassical transmitted state differs only slightly from what it would be were a certain equivalent classical state transmitted instead. The implications for remote communications are discussed.
The general problem of performance advantage obtainable by the use of nonclassical transmitted states over classical ones is considered. Attention is focused on the situation where system loss is significant and additive Gaussian noise may be present at the receiver. Under the assumption that the total received state is classical, rigorous output density operator representations and their trace distance bounds are developed for classical and nonclassical transmitted states. For applications with high loss in all modes, a practical no-go theorem is enunciated that rules out the possibility of significant advantage of nonclassical over classical states. The recent work on quantum illumination is discussed as an example of our no-go approach.
A phase space for the single-mode light field is constructed by using optical phase variables. This phase-space formalism is directly connected to optical-phase-related operators. The phase-state basis \ensuremath{\Vert}\ensuremath{\theta}〉 is used to represent various quantum operators and states. Properties of the density operator \ensuremath{\rho}^ phase-state matrix elements P(\ensuremath{\theta},\ensuremath{\theta}')=〈\ensuremath{\theta}\ensuremath{\Vert}\ensuremath{\rho}^\ensuremath{\Vert}\ensuremath{\theta}'〉 and their relations to phase-related quasiprobability distributions are discussed. By using the phase representation, different types of number-phase intelligent states are analyzed.
When the phase of the transmittance between a unimodal transmitter and a unimodal receiver is uniformly distributed over(0,2\pi), the density operator of the received signal field commutes with the photon number operator, and the optimum detector of the signal counts photons. A simple formula is given for the probability generating function of the number of photons in terms of the quasi-probability distribution of the transmitted signal. It is used to determine the average error probability of an on-off binary communication system transmitting two-photon coherent-state signals, received in the presence of thermal noise.
We propose a definition of nonclassicality for a single-mode quantum-optical process based on its action on coherent states. If a quantum process transforms a coherent state to a nonclassical state, it is verified to be nonclassical. To identify nonclassical processes, we introduce a representation for quantum processes, called the process-nonclassicality quasiprobability distribution, whose negativities indicate nonclassicality of the process. Using this distribution, we derive a relation for predicting nonclassicality of the output states for a given input state. We experimentally demonstrate our method by considering the single-photon addition as a nonclassical process and predicting nonclassicality of the output state for an input thermal state.