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.
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.
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.
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.
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.
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.
A method is given for calculating the minimum average error probability attainable in deciding between a mixed state and a pure state of a quantum system. It is applied, first, to the detection of a noisy coherent pulse represented by a state with a Gaussian P-representation and, second, to the detection of a signal represented at the transmitter by a two-photon coherent state (TCS). In both problems the field of the receiver is free of background noise and, when no signal was transmitted, is in the ground state.
The fundamental performance limits and channel capacity of optical communications systems operating over the free-space channel will be examined using quantum detection theory. The performance of the optimum quantum receiver for on{ofi keying and optical binary phase-shift keying is flrst examined as a pure-state (no-noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes will be evaluated for the optimum quantum receiver by making use of the concept of quantum measurement states. The performance of M-ary pulse-position modulation, which requires a product state representation, will be evaluated along with the performance of certain dense signal sets. Performance comparisons with classical techniques show an improvement of over 5 dB in some cases when quantum detection is employed. As a further application of the quantum detection theory, the capacity of the binary channel with on{ofi keyed modulation and quantum detection is evaluated and shown to exceed the capacity obtained with classical photon counting.