Biphoton ququarts as either pure or mixed states, features and reconstruction from coincidence measurements

Abstract

Features of biphoton polarization-frequency ququarts are considered. Their wave functions are defined as functions of both polarization and frequency variables of photons with the symmetry obligatory for two-boson states taken into account. In experiments, biphoton ququarts can display different features in dependence on whether experiments involve purely polarization or (alternatively) polarization-frequency measurements. If in experiments one uses only polarization measurements, the originally pure states of ququarts can be seen as mixed biphoton polarization states. Features of such states are described and discussed in details. Schemes of coincidence measurements for reconstruction of the ququart's parameters are suggested and described.

Three-photon polarization ququarts: polarization, entanglement and Schmidt decompositions

“…For choosing one of these two solutions, additional, measurements can be needed, with polarizers turned for some angle α ≠ 0, 45°. For BPQ similar sets of measurements providing determination of phases were discussed in [35] A much simpler scheme of measurements can be used for finding parameters of TPPQ which can be reduced to the form (33). Both this form and a scheme of its measurement (figure 10) indicate a deep analogy between the TPPQ of the type (33) and BPQ [25,26].…”