Projection methods in quantum information science

摘要: We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set states $\{\rho_1, \dots, \rho_k\}$ to another such $\{\hat\rho_1, \hat\rho_k\}$. In other words, we must find {\em completely positive linear map}, it exists, maps density matrices matrices. This problem, in turn, is an instance semi-definite feasibility but with highly structured constraints. The nature constraints makes projection based algorithms very appealing when number variables huge and standard interior point-methods for programming are not applicable. provide emperical evidence this effect. moreover present heuristics finding both high rank low solutions. Our experiments on \emph{method alternating projections} \emph{Douglas-Rachford} reflection method.