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Abstract: The quantum coding theorem proved in 1996 independently by A.S. Holevo, B. Schumacher and M.D. Westmoreland sets an upper bound on the number of states of a quantum system that can be used to encode classical information, so that the information can be asymptotically accurately restored after transmission. Such the quantity is known as a classical capacity of quantum channel. Due to the presence of entangled states in a composite quantum system that are not simple tensors, calculating the classical capacity turned out to be an extremely technically difficult task. An important example is given by channels generated by projective unitary representations of finite groups. This class includes Weyl channels, which, in turn, cover all unital qubit channels. Recently I found examples of channels belonging to this class for which the classical capacity can be calculated explicitly. The proof relies on the Karamata majorization method for probability distributions.
Bio: Dr. Grigory Amosov is a Leading Scientific Researcher at Steklov Mathematical Institute of RAS. His research interests are non-commutative probability theory and its applications in quantum theory of information and statistical decisions.
