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arXiv:quant-ph/0309096 · Journal of Optics B Quantum and Semiclassical Optics

Binary optical communication in single-mode and entangled quantum noisy channels

Stefano Olivares, Matteo G. A. Paris

Published Nov 5, 2003• 31 citations
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Abstract

We address binary optical communication in single-mode and entangled quantum noisy channels. For single mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs during both the propagation and the detection of the signals. We then consider entangled channels based on a twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison with the single-mode cases for a large range of values of quantum efficiency and noise parameters.

DOI
10.1088/1464-4266/6/1/012

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We address binary optical communication in single-mode and entangled quantum noisy channels. For single mode we present a systematic comparison between direct photodetection and homodyne detection in realistic conditions, i.e. taking into account the noise that occurs during both the propagation and the detection of the signals. We then consider entangled channels based on a twin-beam state of radiation, and show that with realistic heterodyne detection the error probability at fixed channel energy is reduced in comparison with the single-mode cases for a large range of values of quantum efficiency and noise parameters.
The description of Gaussian noise for single-mode quantum fields is briefly reviewed and applied to calculate the maximal information properties of three quantum communication channels degraded by Gaussian noise. These channels are based on (i) heterodyne detection of coherent states, (ii) homodyne detection of squeezed states, and (iii) photodetection of number states. It is found that each channel can outperform the others for a given noise level, where the optimum channel is essentially determined by the product of the average noise and signal energies.
A quantum-communication-theoretical approach to the homodyne-direct receiver is presented and used to obtain the quantum detection operators and average probability of error for any binary quantum-state signal. The effect of the quantum efficiency η of a photodetector used in the receiver is taken into account. Which quantum states have been received is determined by comparing the read-out of the receiver with a certain decision level; so the dependences of the detection operators and average probability of error on a decision level are also considered. As a quantum-state signal, the binary phaseshift keyed signal including thermal noise is investigated in detail, and the condition necessary for the average probability of error of the homodyne-direct receiver to be smaller than the standard quantum limit (the short noise limit) of the signal detection is obtained.
Communication theory applied to lightwave channels is ordinarily carried out using the semiclassical theory of photodetection. Recent development of nonclassical light sources-whose photodetection statistics require the use of quantum theory-plus increasing interest in optics-based approaches to quantum information processing necessitates a thorough understanding of the similarities and distinctions between the semiclassical and quantum theories of optical communications. This paper is addressed to that need, focusing, for convenience, on the free-space communication channel using Gaussian states of light. The quantum version of the Huygens-Fresnel diffraction integral is reviewed, along with the semiclassical and quantum theories of direct, homodyne, and heterodyne detection. Maximally entangled Gaussian state light is used, in conjunction with quantum photodetection theory, to explain the nonclassical effects seen in Hong-Ou-Mandel interferometry and violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality. The classical information capacities of several bosonic channels are reviewed, and shown to exceed what can be achieved using conventional optical receivers.
The determination of the quantum properties of a single-mode radiation field by heterodyne or double homodyne detection is studied. The realistic case of not fully efficient photodetectors is considered. It is shown that a large amount of quite precise information is available, whereas the completeness of such information is also discussed. Some examples are given and the special case of states expressed as a finite superposition of number states is considered in some detail. \textcopyright{} 1996 The American Physical Society.
The theory of balanced homodyne and heterodyne detection is developed for inputs in which the signal field is in an arbitrary quantum state and the local-oscillator field is in a highly excited coherent state. Exact expressions are derived for the photocount moment-generating functions in the special case of a coherent signal. For more general signals, the first two moments of the photocount probability distribution are determined. The moments are evaluated for the examples of a coherent signal with a chaotic noise component, and for squeezed light derived from a degenerate and from a non-degenerate parametric amplifier. The corresponding moments for direct detection are obtained so that comparisons can be made. The Kelley-Kleiner photocount distribution formula is adapted to balanced detection schemes. Light beams are characterized throughout by their energy fluxes, and the theory accordingly describes steady-state experiments.