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YuenLam Cheung (vris.cheunggmail.com) Abstract: We consider the problem of constructing quantum operations or channels, if they exist, that transform a given set of quantum states $\{\rho_1, \dots, \rho_k\}$ to another such set $\{\hat\rho_1, \dots, \hat\rho_k\}$. In other words, we must find a {\em completely positive linear map}, if it exists, that maps a given set of density matrices to another given set of density matrices. This problem, in turn, is an instance of a positive semidefinite feasibility problem, but with highly structured constraints. The nature of the constraints makes projection based algorithms very appealing when the number of variables is huge and standard interior pointmethods for semidefinite programming are not applicable. We provide empirical evidence to this effect. We moreover present heuristics for finding both high rank and low rank solutions. Our experiments are based on the \emph{method of alternating projections} and the \emph{DouglasRachford} reflection method. Keywords: quantum operations, completely positive linear maps, alternating projection methods, DouglasRachford method, Choi matrix, semidefinite feasibility problem, large scale Category 1: Linear, Cone and Semidefinite Programming Category 2: Other Topics (Other ) Citation: University of Waterloo, July/14 Download: [PDF] Entry Submitted: 07/23/2014 Modify/Update this entry  
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