Reaching the quantum Cramér-Rao bound of transmission measurements

Presenting Author: Timothy Woodworth, University of Oklahoma
Contributing Author(s): Carla Hermann-Avigliano, Kam Wai Clifford Chan, Alberto Marino

The quantum Cramér-Rao bound (QCRB) is commonly used to quantify the lower bound for the uncertainty in the estimation of a given parameter. Here, we calculate the QCRB for transmission measurements of an optical system probed by a beam of light. Estimating the transmission of an optical element is important as it is required for the calibration of optimal states for interferometers, characterization of high efficiency photodetectors, or as part of other measurements, such as those in plasmonic sensors or in ellipsometry. We use a beam splitter model for the losses introduced by the optical system to calculate the QCRB for different input states. We compare the bound for a coherent state, a two-mode squeezed-state (TMSS), and a Fock state. We prove that the Fock state gives the lowest possible uncertainty in estimating the transmission for any state and demonstrate that the TMSS approaches this ultimate bound for large levels of squeezing. Finally, we show that a simple measurement strategy for the TMSS, namely an intensity difference measurement, is able to saturate the QCRB. We then perform experiments to show this.

(Session 7 : Friday from 11:30am-12:00pm)


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