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IEEE International Conference on Acoustics Speech and Signal Processing

Digital communication and quantum phase detection

Michael J. W. Hall, Ian Fuss, L.B. White

Published Jan 1, 1991• 0 citations
Publisher

Abstract

A theory of symmetric phase shift keying is developed using quantum mechanics. The minimum average probability of error is then determined for phase-shift-keyed optical communication systems which use physical states. It is shown that this minimum error is achieved by using states which are represented in the number state basis by discrete prolate spheroidal sequences.>

DOI
10.1109/icassp.1991.150770

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A theory of symmetric phase shift keying is developed using quantum mechanics. The minimum average probability of error is then determined for phase-shift-keyed optical communication systems which use physical states. It is shown that this minimum error is achieved by using states which are represented in the number state basis by discrete prolate spheroidal sequences.>
A canonical description of electromagnetic phase, related to both the Susskind-Glogower and Pegg-Barnett phase formalisms is applied to determine the quantum limits for digital communication based on phase detection. It is proved that canonical phase detection is superior to all other shift-invariant phase detection methods, in its ability to accurately resolve signals into phase bins under any given energy constraint. Under a bounded energy constraint, the optimal signal states are characterized in terms of discrete prolate spheroidal sequences and an asymptotic formula is given for the minimum error rate. Numerical results are given to provide comparison between canonical and heterodyne phase detection. A new method of deriving the statistics of (ideal) heterodyne detection for a given image-band field is presented.
We develop a theory of quantum M-ary phase shift keying in which quantum states of optical modes are modulated at the transmitter by applying one of M uniformly-spaced phase shifts. We allow full freedom in choosing modulation states with any number of signal, i.e., transmitted, and ancilla modes, subject only to an average energy, i.e., photon number, constraint in either the signal modes alone or in the signal and ancilla modes together. For lossless operation and unrestricted POVM measurements at the receiver, we find the explicit form of the modulation state that minimizes the average error probability under an energy constraint of N photons. Multiple signal modes, mixed states, and entanglement with an ancilla are shown to be unnecessary for optimum performance. We show that communication with zero error is possible if and only if N ≥ (M - 1)/2.
In this paper, we investigate the symbol error probability (SEP) of phase-squeezed M-ary phase-shift keying (M-PSK). Since the relevant observable for M-PSK detection is the optical phase, we adopt the adaptive Mark-II receiver which is a physically realizable phase measurement. First, we develop a theoretical analysis based on the phase probability operator measure (POM) of the Mark-II scheme in the Fock basis. Then, we develop two SEP methods based on the statistics of the received PSK symbol and the error introduced by the Mark-II measurement. The first method derives the phase probability density induced by the squeezed state noise and incorporates the additional Mark-II phase uncertainty through an angular convolution. Since this convolution does not admit a simple closed form, we also introduce an effective tangential-variance model, which yields a closed form SEP expression in terms of the Owen's T-function. Numerical results show that phase squeezing substantially reduces the SEP of M-PSK compared to coherent state transmission, with greater gains for higher constellation orders. Notably, for the investigated scenario, squeezing can almost double the photon efficiency of M-PSK as the mean number of transmitted photons increases. Finally, the proposed approximations closely follow the Mark-II POM analysis, typically within an accuracy of 2-4 photons, and therefore provide accurate and computationally efficient tools for analyzing phase squeezed quantum M-PSK communication.
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.
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-off keying (OOK) and optical binary phase shift keying (BPSK) is first examined as a pure state (no noise) problem. The classical capacity of the binary symmetric channel for these two modulation schemes is then 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, is evaluated along with the performance of certain 'dense signal sets.' Performance comparisons with classical techniques shows over 5 dB improvement 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-off keyed modulation and quantum detection is evaluated, and shown to exceed the capacity obtained with classical photon counting.