Formalism of two-time tensors for describing quantum states under post-selection conditions

A generalization of the two-state density vector formalism for the case of postselection described by an arbitrary effect of a positive operator-valued measure is obtained. It is shown that the standard formalism, which does not take postselection into account, and the two-vector formalism are the limiting special cases of the new formalism. New schemes for tomography of states under post-selection conditions are proposed, the operability of which is demonstrated by the example of experimental observation of the time-reversal propagation of a quantum state in the quantum teleportation protocol.