Transmission Estimation at the Fundamental Quantum Cramér-Rao Bound with Macroscopic Quantum Light

Abstract

The field of quantum metrology seeks to apply quantum techniques and/or resources to classical sensing approaches with the goal of enhancing the precision in the estimation of a parameter beyond what can be achieved with classical resources. Theoretically, the fundamental minimum uncertainty in the estimation of a parameter for a given probing state is bounded by the quantum Cramér-Rao bound. From a practical perspective, it is necessary to find physical measurements that can saturate this fundamental limit and to show experimentally that it is possible to perform measurements with the required precision to do so. Here we perform experiments that saturate the quantum Cramér-Rao bound for transmission estimation over a wide range of transmissions when probing the system under study with a bright two-mode squeezed state. To properly take into account the imperfections in the generation of the quantum state, we extend our previous theoretical results to incorporate the measured properties of the generated quantum state. For our largest transmission level of 84%, we show a 62% reduction over the optimal classical protocol in the variance in transmission estimation when probing with a bright two-mode squeezed state with 8 dB of intensity-difference squeezing. Given that transmission estimation is an integral part of many sensing protocols, such as plasmonic sensing, spectroscopy, calibration of the quantum efficiency of detectors, etc., the results presented promise to have a significant impact on a number of applications in various fields of research.

Optimal transmission estimation with dark counts

“…Quantum metrology promises improvements in estimation precision relative to classical probes and measurement devices using a comparable amount of resources [1][2][3][4][5][6][7][8][9][10][11]. These advantages are present in transmission estimation and mathematically equivalent problems [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29] and have been experimentally demonstrated on numerous occasions [30][31][32][33][34][35][36][37][38][39][40][41][42][43], with applications including ellipsometry [44][45][46], spectroscopy [47][48]…”

Multiparameter transmission estimation at the quantum Cramér–Rao limit on a cloud quantum computer

“…In these circumstances, specially designed quantum probes and detectors can decrease the parameter estimate's variance by the fraction of light lost [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41], due to the increased correlations in their photon-number distributions, which is particularly useful in the sensing of increasingly faint signals such as when a trace amount of a substance absorbs a small amount of light from a particular electromagnetic field mode. These quantum advantages have been demonstrated using either single photons [42][43][44][45][46][47][48] or squeezed light [24,31,37,[49][50][51][52][53][54] as probe states.…”