Search

Measurement and discrimination of quantum states are essential tasks in quantum information processing. A measurement strategy consisting of photon detection preceded by a displacement operation, that is actively feedback-controlled depending on the photon detection outcomes, is known to be a powerful measurement technique for quantum state discrimination [1] . In our work, we experimentally develop such a feedback measurement with photon detection and characterize its positive operator valued measure (POVM) via quantum detector tomography using coherent states. Quantum detector tomography has been demonstrated for various types of static measurements [3] , but not before for a dynamically updated measurement. As a potential application of the feedback measurement for quantum state discrimination, we analyze the performance of our measurement for the discrimination of the two orthogonal superpositions of vacuum and single photon states $| \pm \rangle = (|0\rangle \pm |1\rangle )/\sqrt 2 $ , which are the conjugate basis states of the optical single-rail qubit.

We propose quantum receivers with optical squeezing and photon-number-resolving detectors (PNRDs) for the near-optimal discrimination of quaternary phase-shift-keyed coherent state signals. The basic scheme is similar to the previous proposals [e.g., Izumi et al., Phys. Rev. A 86, 042328 (2012)] in which displacement operations, on-off detectors, and electrical feedforward operations were used. Here we study two types of receivers, one of which installs optical squeezings and the other uses PNRDs instead of on-off detectors. We show that both receivers can attain lower error rates than that in the previous scheme. In particular, we show the PNRD-based receiver has a significant gain when the ratio between the mean photon number of the signal and the number of the feedforward steps is relatively high, in other words, when the probability of detecting two or more photons at each detector is not negligible. Moreover, we show that the PNRD-based receiver can suppress the errors due to dark counts, which the receiver with the on-off detector cannot do with a small number of feedforwards.