Quantum Metrology for Noisy Systems

Abstract

The estimation of parameters characterizing dynamical processes is a central problem in science and technology. It concerns for instance the evaluation of the duration of some interaction, of the value of a coupling constant, or yet of a frequency in atomic spectroscopy. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of probes or the probing energy). For independent probes, it scales as 1/ √ N-the standard limit-a consequence of the central-limit theorem. Quantum strategies, involving for instance entangled or squeezed states, may improve the precision, for noiseless processes, by an extra factor 1/ √ N, leading to the so-called Heisenberg limit. For noisy processes, an important question is if and when this improvement can be achieved. Here, we review and detail our recent proposal of a general framework for obtaining attainable and useful lower bounds for the ultimate limit of precision in noisy systems. We apply this bound to lossy optical interferometry and show that, independently of the initial states of the probes, it captures the main features of the transition, as N grows, from the 1/N to the 1/ √ N behavior.

Maximal quantum Fisher information for general su(2) parametrization processes

“…The past two decades have witnessed a dramatic development of quantum metrology [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], which is rooted in the theory of quantum parameter estimation. The estimation of unknown parameters plays an important role in physics and engineering.…”

Ultimate sensitivity of precision measurements with intense Gaussian quantum light: A multimodal approach

“…However, in the present state of technology real measurement schemes using these states do not lead to very high sensitivities, because of the small values of N experimentally reachable (so far, the highest achievable NOON state has N ∼ 100 [8]), and decoherence tends to rapidly destroy these states, therefore limiting the performance of the measurement to a 1/N 1/2 scaling for large N [9][10][11]. In [12] a scheme was proposed that reaches the HL without the use of an entangled state.…”

“…The modes v n do not depend on θ since the derivative in (11) has been taken at the value θ = 0 The expression of the Fisher information in the { v i (r, t)} mode basis is very simple as it involves only one matrix element of Γ −1 θ :…”

Enhancement of frequency estimation by spatially correlated environments

“…Although taking advantage of entanglement in quantum protocols improves the precision of estimation, it makes the protocoles very sensitive to noise. Hence, it is important to investigate the restrictions which are dictated on the ultimate achievable precision by the dynamics arising from the presence of an environment [12][13][14]. According to the scale of correlation times during which correlations disappear, noises can be grouped into Markovian and nonMarkovian types.…”