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For a known weak signal in additive white noise, the asymptotic performance of a locally optimum processor (LOP) is shown to be given by the Fisher information (FI) of a standardized even probability density function (PDF) of noise in three cases: (i) the maximum signal-to-noise ratio (SNR) gain for a periodic signal; (ii) the optimal asymptotic relative efficiency (ARE) for signal detection; (iii) the best cross-correlation gain (CG) for signal transmission. The minimal FI is unity, corresponding to a Gaussian PDF, whereas the FI is certainly larger than unity for any non-Gaussian PDFs. In the sense of a realizable LOP, it is found that the dichotomous noise PDF possesses an infinite FI for known weak signals perfectly processed by the corresponding LOP. The significance of FI lies in that it provides a upper bound for the performance of locally optimum processing.
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Quantum information science is an exciting, wide, rapidly progressing, cross-disciplinary field, and that very nature makes it both attractive and hard to enter. In this primer, we first provide answers to the three essential questions that any newcomer needs to know: How is quantum information represented? How is quantum information processed? How is classical information extracted from quantum states? We then introduce the most basic quantum information theoretic notions concerning entropy, sources, and channels, as well as secure communications and error correction. We conclude with examples that illustrate the power of quantum correlations. No prior knowledge of quantum mechanics is assumed.
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