Naimark extension for the single-photon canonical phase measurement
Nicola Dalla Pozza, Matteo G. A. Paris · Physical Review A · 2019
We address the implementation of the positive-operator-valued measure (POVM) describing the optimal $M$-outcome discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by the Naimark theorem; then the resulting projective measure is implemented by a Knill-Laflamme-Milburn scheme involving an optical network and photon counters. We find the analytical expression of the Naimark extension and the detection scheme that realizes it for an arbitrary number of outcomes $M={2}^{N}$.