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IEEE Transactions on Information Theory

Optical communication with two-photon coherent states--Part III: Quantum measurements realizable with photoemissive detectors

Horace P. Yuen, Jeffrey H. Shapiro

Published Jan 1, 1980• 637 citations
Publisher

Abstract

In Part I of this three-part study it was shown that the use of two-photon coherent state (TCS) radiation may yield siginificant performance gains in free-space optical communicatinn if the receiver makes a quantum measurement of a single field quadrature. In Part II it was shown that homodyne detection achieves the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes the linear modulation TCS performance gain found in Part I. Furthermore, it was shown in Part il that ff homodyne detection does exactly correspond to the field quadrature measurement, then a large binary communication performance gain is afforded by homodyne detection of antipodal TCS signals. The full equivalence of honmdyne detection and single-quadrature field measurement, as well as that of heterodyne detection and two-quadrature field measurement, is established. Furthermore, a heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. This coafiguration termed TCS heterodyne detection is shown to realize all the quantum measurements described by arbitrary TCS. The foregoing results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.

DOI
10.1109/tit.1980.1056132

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In Part I of this three-part study it was shown that the use of two-photon coherent state (TCS) radiation may yield siginificant performance gains in free-space optical communicatinn if the receiver makes a quantum measurement of a single field quadrature. In Part II it was shown that homodyne detection achieves the same signal-to-noise ratio as the quantum field quadrature measurement, thus providing a receiver which realizes the linear modulation TCS performance gain found in Part I. Furthermore, it was shown in Part il that ff homodyne detection does exactly correspond to the field quadrature measurement, then a large binary communication performance gain is afforded by homodyne detection of antipodal TCS signals. The full equivalence of honmdyne detection and single-quadrature field measurement, as well as that of heterodyne detection and two-quadrature field measurement, is established. Furthermore, a heterodyne configuration which uses a TCS image-band oscillator in addition to the usual coherent state local oscillator is studied. This coafiguration termed TCS heterodyne detection is shown to realize all the quantum measurements described by arbitrary TCS. The foregoing results are obtained by means of a representation theorem which shows that photoemissive detection realizes the photon flux density measurement.
In Part I of this three-part study, it was shown that novel quantum states, called two-photon coherent states (TCS), have significant potential for improving free-space optical communications. Because TCS radiation does not possess a classical analog, i.e., its diagonalP-representation is highly singular, the semiclassical conditional Poisson process model for direct detection is not applicable to TCS reception. In this paper, photoemissive detection of arbitrary quantized radiation fields is studied with incorporation of the nontrivial effects of detector quantum efficiency. General theorems are derived permitting the application of classical point process results to the detection and estimation of signals in arbitrary quantum states. These general theorems are applied to determining the performance of TCS optical communication systems that employ direct, heterodyne, or homodyne detection in binary decision as well as in linear modulation problems. It is shown that the use of TCS radiation with direct detection or heterodyne detection results in minimal performance increments over comparable coherent-state systems. Homodyne detection, however, can achieve the full TCS signal-to-noise ratio improvement predicted in Part I of this study. The increase in homodyne signal-to-noise ratio obtained by use of TCS radiation yields significant performance gains in both linear modulation and antipodal signal detection.
Recent theoretical work has shown that novel quantum states, called two-photon coherent states (TCS), have significant potential for improving free-space optical communications. The first part of a three-part study of the communication theory of TCS radiation is presented. The issues of quantum-field propagation and optimum quantum-state generation are addressed. In particular, the quantum analog of the classical paraxial diffraction theory for quasimonochromatic scalar waves is developed. This result, which describes the propagation of arbitrary quantum states as a boundary-value problem suitable for communication system analysis, is used to treat a number of quantum transmitter optimization problems. It is shown that, under near-field propagation conditions, a TCS transmitter maximizes field-measurement signal-to-noise ratio among all transmitter quantum states; the performance of the TCS system exceeds that for a conventional (coherent state) transmitter by a factor ofN_{s} + 1, whereN_{s}is the average number of signal photons (transmitter energy constraint). Under far-field propagation conditions, it is shown that use of a TCS local oscillator in the receiver can, in principle, attenuate field-measurement quantum noise by a factor equal to the diffraction loss of the channel, if appropriate spatial mode mixing can be achieved. These communcation results are derived by assuming that field-quadrature quantum measurement is performed. In part II of this study, photoemissive reception of TCS radiation will be considered; it will be shown therein that homodyne detection of TCS fields can realize the field-quadrature signal - to-noise ratio performance of part I. In part III, the relationships between photoemissive detection and general quantum measurements will be explored. In particular, a synthesis procedure will be obtained for realizing all the measurements described by arbitrary TCS.
The performance of two-photon coherent-state (TCS) signals and integral-quantum signals in unimodal and bimodal free-space optical communications is compared with that of ordinary ,coherent signals under the constraint of fixed average error probability. For the unimodal channel of known phase the minimum attainable error probability for both on-off and antipodal TCS signals received in thermal noise is calculated by applying perturbation theory to the detection operator equation. For unimodal antipodal TCS signaling the threshold receiver is also considered. For channels of random phase the optimum photon-counting receiver is analyzed. In all cases the advantage of the nonclassical signal over an ordinary coherent signal vanishes as the transmittance of the channel goes to zero.
We present an application of coherent homodyne detection to the problem of low photon number communications and cryptography. As the coherent demodulation of an optical field requires the measurement of its (non commutating) inphase and quadrature components, we present the structure and operation of an 8-port optical hybrid comprising 2 balanced homodyne detection structures, for the simultaneous measurement of the 2 quadratures. We analyze this receiver operating with a strong local oscillator field, when the received field is in weak coherent states, with digital phase modulation: we obtain the homodyne statistics and the uncertainty product in the presence of vacuum noises from the input signal port and unused ports and discuss the increase in uncertainty due to the simultaneous measurements of the quadratures. We obtain the signal to noise ratio as well of the bit error rate performance for binary phase shift keying and discuss the departure from the standard quantum limit.
Homodyne detection is the most effective detection scheme employed in quantum optics to characterize quantum states. It is based on mixing at a beam splitter the signal to be measured with a coherent state, called the “local oscillator,” and on evaluating the difference of the photocurrents of two photodiodes measuring the outputs of the beam splitter. If the local oscillator is much more intense than the field to be measured, the homodyne signal is proportional to the signal-field quadratures. If the local oscillator is less intense, the photodiodes can be replaced with photon-number-resolving detectors, which have a smaller dynamics but can measure the light statistics. The resulting new homodyne-like detector acquires a hybrid nature, being it capable of yielding information on both the particle-like (statistics) and wave-like (phase) properties of light signals. The scheme has been tested in the measurement of the quadratures of coherent states, bracket states and phase-averaged coherent states at different intensities of the local oscillator.
The main topic of this contract is on the communication theoretic aspects of TCS (Two-photon coherent states) systems. The optimality of TCS has been shown as transmitter quantum states, in a number of linear modulation and binary detection problems. A theory of quantum field propagation has also been developed which is essential for a correct analysis of TCS behavior in optical transmission systems. In particular, the difference between near-field and far-field TCS communication is now understood.