As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often considered as a basic yet important problem in various applications. Typical examples include but are not limited to optimizing the likelihood functions in quantum measurement tomography, searching the Bell parameters in Bell-test experiments, and calculating the capacities of quantum channels. In this work, we propose reliable algorithms for optimizing arbitrary functions over the space of quantum measurements by combining the so-called Gilbert’s algorithm for convex optimization with certain gradient algorithms. With extensive applications, we demonstrate the efficacy of our algorithms with both convex and nonconvex functions.

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In according to the issue of multi-signal jamming in communication reconnaissance, single channel signal separation for multi-GMSK signals has been studied with a method based on MLP. With parameters of Doppler-shift, time-delay, amplitude and coding sequences efficiently estimated, signals could be restructured, and then be separated. Simulations have proved well separation results can be obtained with the method for unequal power signals with certain SNRs.