Evaluation of polarization entanglement generated by pulsed spontaneous parametric down-conversion with multi-pairs using four single-photon detectors for quantum state tomography

Quantum state tomography (QST) is widely used to evaluate entanglement generated by spontaneous parametric down-conversion. Two-fold coincidence counts for 16 different configurations have been measured using single-photon detectors to estimate the fidelity (i.e., the probability overlap between ideal and real states) from the reconstructed density matrix. However, multi-pair emission events degrade the fidelity. Here, we numerically analyze pulse-pumped polarization-entangled photon pairs for single-photon detectors that can or cannot count the number of incident photons to estimate the fidelity given by QST. Threshold single-photon detectors are desirable for QST from a practical point of view. Our analysis suggests that using four threshold single-photon detectors for two-fold coincidence measurements offers almost the same fidelity as that given by four photon-number-resolving single-photon detectors. The fidelity estimated by QST becomes poor and loss independent when two threshold single-photon detectors are used.