Approximate Computation of States with Minimal Dispersion in KuryshkinWodkiewicz Quantum Mechanics The transfer of quantum information via quantum communication channels necessarily includes the process of quantum measurements of output. If we ignore the full description of the functioning of such channels, and focus only on the procedure of quantum measurements, we should work with the most mathematically rigorous standard Holevo model of quantum measurements. The KuryshkinWodkiewicz quantum mechanics is a constructive version of the standard model, which includes a description of the phase representation of quantum mechanics. The longest living pure states in the dissipative quantum model under study are states with minimal dispersion. The work is devoted to an approximate numerical solution of the problem of finding such states.

Computing ClassicalQuantum Channel Capacity Using Blahutxe2x80x93Arimoto Type Algorithm: A Theoretical and Numerical Analysis Based on Arimotoxe2x80x99s work in 1972, we propose an iterative algorithm for computing the capacity of a discrete memoryless classicalquantum channel with a finite input alphabet and a finite dimensional output, which we call the Blahutxe2x80x93Arimoto algorithm for classicalquantum channel, and an input cost constraint is considered. We show that, to reach    e    accuracy, the iteration complexity of the algorithm is upper bounded by      log n log e  e     where n is the size of the input alphabet. In particular, when the output state        xcfx81 x     x xe2x88x88 X      is linearly independent in complex matrix space, the algorithm has a geometric convergence. We also show that the algorithm reaches an    e    accurate solution with a complexity of     O (    m 3  log n log e  e  )    , and     O (  m 3  log e  log  ( 1  xcexb4 )    e  D (  p *     p  N 0   )   )     in the special case, where m is the output dimension,     D (  p *     p  N 0   )     is the relative entropy of two distributions, and    xcexb4    is a positive number. Numerical experiments were performed and an approximate solution for the binary twodimensional case was analysed.