Sinposis

These applications include quantum measuring, quantum information theory, quantum communication theory, quantum sensing, quantum signal processing, quantum computing, quantum cryptography, and quantum machine learning. Although some of the probabilistic methods differ in machine learning disciplines from those in the quantum technologies, many techniques are very similar. Probability is introduced in the text rigorously, in Komogorov's vision. It is however, slightly modified by developing the theory in a Many-Sorted Algebra setting. Both deep learning and quantum technologies have several probabilistic and stochastic methods in common. Concepts in entropy are provided from a Shannon as well as a von-Neumann view. presented in the Schmidt decomposition. Besides the in-common methods, Born's rule as well as positive operator valued measures are described and illustrated, along with quasi-probabilities.