Structural physical approximations of unphysical maps and generalized quantum measurements

We investigate properties of the structural physical approximation (SPA) of the partial transposition map recently introduced by Horodecki and Ekert [Phys. Rev. Lett. 89, 127902 (2002)]. 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 the preparation of a suitable output state. We also introduce SPA for a 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