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The precision in phase measurement is determined by the number of resources that are used. The minimum uncertainty that can be achieved with uncorrelated resources is the shot-noise limit (SNL), while the ultimate precision limit set by quantum mechanics is the Heisenberg limit (HL). First, we will discuss the task of phase sensing, which deals with determining small deviations in a phase about an already known value. Despite theoretical proposals stretching back decades, no measurement using photonic (i.e. definite photon number) states has unconditionally surpassed the SNL in phase sensing. Previous demonstrations employed postselection to discount photon loss in the source, interferometer or detectors. In our demonstration we used the state-of-art single photon generation and detection technology to respectively make and measure a two-photon NOON state and use it to perform unconditional phase sensing beyond the SNL — that is, without artificially correcting for loss or any other source of imperfection.
Next, we present an experimental demonstration of a new protocol for the ab-initio phase estimation, where the goal is to measure a completely unknown optical phase. Until now, and despite intense theoretical attention, no technique has been proposed or implemented for such a measurement with ultimate precision, at the exact HL. Our measurement protocol combines several approaches, such as entanglement, multiple applications of the phase shift and simulated adaptive measurement. With it we experimentally realized the optimal phase measurement scheme for three resources, achieving a precision within 4% of the exact HL (postselected on detected coincidence counts, in this case).
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