Description of quantum states in postselection experiments

Postselection is an important practical tool in modern quantum information technologies. In the special case of preparation (preselection) and postselection with respect to pure states, the effective quantum state realized in the experiment can be described using the two-state vector formalism. The report will consider the construction of a general time-bidirectional state formalism, which includes both the two-state vector formalism and the traditional formalism of density matrices, as limiting special cases. The question about experimental reconstruction (tomography) of states in this formalism will be considered. An example of the use of the developed formalism within the experimental observation of a continuous space-time trajectory of a quantum state propagation in the quantum teleportation protocol will also be presented.