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We address the implementation of the positive operator-valued measure (POVM) describing the optimal M-outcomes discrimination of the polarization state of a single photon. Initially, the POVM elements are extended to projective operators by 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 realise it for an arbitrary number of outcomes M = 2^N.
We analyze the optimal state, as given by Berry and Wiseman [Phys. Rev. Lett {bf 85}, 5098, (2000)], under the canonical phase measurement in the presence of photon loss. The model of photon loss is a generic fictitious beam splitter, and we present
We revisit the problem of finding the Naimark extension of a probability operator-valued measure (POVM), i.e. its implementation as a projective measurement in a larger Hilbert space. In particular, we suggest an iterative method to build the project
Much of modern metrology and communication technology encodes information in electromagnetic waves, typically as an amplitude or phase. While current hardware can perform near-ideal measurements of photon number or field amplitude, to date no device
While the phase of a coherent light field can be precisely known, the phase of the individual photons that create this field, considered individually, cannot. Phase changes within single-photon wave packets, however, have observable effects. In fact,
Path-entangled multi-photon states allow optical phase-sensing beyond the shot-noise limit, provided that an efficient parity measurement can be implemented. Realising this experimentally is technologically demanding, as it requires coincident single