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Interplanetary Network Progress Report

Quantum Detection of Binary and Ternary Signals in the Presence of Thermal Noise Fields

Victor A. Vilnrotter, Chi-Wung Lau

Published Oct 1, 2002• 14 citations
OpenAlex

Abstract

A new technique for evaluating the performance of quantum signals observed in the presence of noise is described and evaluated. The quantum theory for detecting coherent-state signals has been developed previously; however, the quantum signal-plus-noise problem has received little attention due to its complexity. Here we develop a discrete approximation to the coherent-state representation of signal-plusnoise density operators, and present solutions to optimum receiver performance in terms of quantum measurement states whose performance is optimized via generalized rotations in Hilbert space. An efficient algorithm for carrying out the required numerical optimization is described and applied to binary signals observed in the presence of noise, for which exact results are available for comparison. The algorithm is then applied to the detection of ternary signals observed in the presence of noise, a previously unsolved problem, and the performance of the optimum receiver is characterized.

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Detection of a coherent quantum signal in thermal noise (Corresp.)

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Methods are presented for calculating the minimum attainable probability of error in detecting a coherent quantum signal received amid thermal noise in the limits of Iow and high signal-to-noise ratio. In the latter limit, quantum-mechanical perturbation theory is applied to solving the detection operator equation approximately. Graphical results are furnished for binary signals transmitted with equal prior probabilities. Previous work on this problem is thus extended to a broader range of signal and noise strengths. The results are applied to the detection of antipodal two-photon-coherent-state signals.

IEEE Transactions on Information Theory•Sep 1, 1979•4 citations
A new technique for evaluating the performance of quantum signals observed in the presence of noise is described and evaluated. The quantum theory for detecting coherent-state signals has been developed previously; however, the quantum signal-plus-noise problem has received little attention due to its complexity. Here we develop a discrete approximation to the coherent-state representation of signal-plusnoise density operators, and present solutions to optimum receiver performance in terms of quantum measurement states whose performance is optimized via generalized rotations in Hilbert space. An efficient algorithm for carrying out the required numerical optimization is described and applied to binary signals observed in the presence of noise, for which exact results are available for comparison. The algorithm is then applied to the detection of ternary signals observed in the presence of noise, a previously unsolved problem, and the performance of the optimum receiver is characterized.
A new technique for evaluating the performance of quantum signals observed in the presence noise is described and evaluated. The quantum theory for detecting coherent-state signals has been developed previously, however the quantum "signal plus noise" problem has received little attention due to its complexity. Here we develop a discrete approximation to the coherent-state representation of signal-plus-noise density operators, and present solutions to optimum receiver performance in terms of quantum "measurement states" whose performance is optimized via generalized rotations in Hilbert space. An efficient algorithm for carrying out the required numerical optimization is described and applied to binary signals observed in the presence of noise, for which exact results are available for comparison. The algorithm is then applied to the detection of ternary signals observed in the presence of noise, a previously unsolved problem, and the performance of the optimum receiver characterized.
A general method for solving an important class of quantum detection problems will be presented and evaluated. The quantum theory for detecting pure states for communications purposes has been developed over two decades ago, however the mixed state problem representing signal plus noise states has received little attention due to its great complexity. Here we develop a practical model for solving the mixed-state problem using a discrete approximation to the coherent-state representation of signal plus noise density operators.
This paper is concerned with the minimax strategy in quantum signal detection theory. First we show a numerical calculation method for finding a solution to the quantum minimax decision problem in the case that the average probability of decision errors is used as the quality function of a quantum communication system. To verify the numerical calculation method, ternary coherent state signal is considered in the absence of thermal noise. After that, the error probability of the quantum minimax receiver for the ternary coherent state signal in the pressure of thermal noise is computed by using this numerical calculation method.
In the literature the performance of quantum data transmission systems is usually evaluated in the absence of thermal noise. A more realistic approach taking into account the thermal noise is intrinsically more difficult because it requires dealing with Glauber coherent states in an infinite-dimensional space. In particular, the exact evaluation of the optimal measurement operators is a very difficult task, and numerical approximation is unavoidable. The paper faces the problem by approximating the P-representation of the noisy quantum states with a large but finite numbers of terms and applying to them the square root measurement (SRM) approach. Comparisons with cases where the exact solution are known show that the SRM approach gives quite accurate results. As application, the performance of quadrature amplitude modulation (QAM) and phase shift keying (PSK) systems is considered. In spite of the fact that the SRM approach is not optimal and overestimates the error probability, also in these cases the quantum detection maintains its superiority with respect to the classical homodyne detection.
Methods are presented for calculating the minimum attainable probability of error in detecting a coherent quantum signal received amid thermal noise in the limits of low and high signal-to-noise ratio. In the latter limit, quantum-mechanical perturbation theory is applied to solving the detection operator equation approximately. Graphic results are furnished for binary signals transmitted with equal prior probabilities. Previous work on this problem is thus extended to a broader range of signal and noise strengths. The results are applied to the detection of antipodal two-photon-coherent-state signals. (Author)
Methods are presented for calculating the minimum attainable probability of error in detecting a coherent quantum signal received amid thermal noise in the limits of Iow and high signal-to-noise ratio. In the latter limit, quantum-mechanical perturbation theory is applied to solving the detection operator equation approximately. Graphical results are furnished for binary signals transmitted with equal prior probabilities. Previous work on this problem is thus extended to a broader range of signal and noise strengths. The results are applied to the detection of antipodal two-photon-coherent-state signals.