Structural physical approximations of unphysical maps and generalized quantum measurements

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We investigate properties of the structural physical approximation (SPA) of the partial transposition map recently introduced by Horodecki and Ekert [quant-ph/0111064]. We focus on the case of two-qubit states and show that in this case the map has the structure of a generalized quantum measurement followed by preparation of a suitable output state. We also introduce SPA for map that transforms two copies of density matrix of a single qubit onto a square of that matrix. We prove that also this map is essentially a generalized quantum measurement.