Ultimate limits for quantum magnetometry via time-continuous measurements

Abstract

We address the estimation of the magnetic field B acting on an ensemble of atoms with total spin J subjected to collective transverse noise. By preparing an initial spin coherent state, for any measurement performed after the evolution, the mean-square error of the estimate is known to scale as 1/J, i.e. no quantum enhancement is obtained. Here, we consider the possibility of continuously monitoring the atomic environment, and conclusively show that strategies based on time-continuous non-demolition measurements followed by a final strong measurement may achieve Heisenberg-limited scaling 1/J 2 and also a monitoring-enhanced scaling in terms of the interrogation time. We also find that time-continuous schemes are robust against detection losses, as we prove that the quantum enhancement can be recovered also for finite measurement efficiency. Finally, we analytically prove the optimality of our strategy.

Non-orthogonal bases for quantum metrology

“…Under certain regularity assumptions, the QFI matrix encodes the ultimate precision bounds on the estimation of unknown parameters encoded in a density matrix (know as quantum Cramer-Rao bounds), while the SLDs and their commutators determine whether such bounds may be saturated with physically realizable measurements [5,6]. The associated applications are plenty, including phase and frequency estimation [4,[7][8][9][10][11][12][13][14][15][16][17], estimation of noise parameters [18][19][20][21][22][23], joint estimation of unitary and/or noisy parameters [24][25][26][27][28][29][30][31], sub-wavelength resolution of optical sources [32][33][34][35][36][37][38], nano-scale thermometry [39][40][41][42][43][44][45], and estimation of Hamiltonian parameters in the presence of phase-transitions [46][47][48]. The most common approach for ...…”

Quantum frequency estimation with conditional states of continuously monitored independent dephasing channels

“…the first equality comes from The identity (14) holds not only for scalars but also when A is an operator or a superoperator, the only crucial property is that the exponential is defined as a power series (and in this case 1 represents the identity operator/superoperator). In particular we will need the following identities…”

“…Continuous measurements have been proposed for different quantum estimation problems, e.g. for magnetometry [10][11][12][13][14], phase tracking [15,16], waveform estimation [17], state estimation and generic dynamical parameters [18][19][20][21][22][23][24][25][26][27][28]. In particular, in our previous paper [29] we have shown the usefulness of continuous monitoring to counteract the effect of noise in frequency estimation.…”

Quantum speed limits under continuous quantum measurements

“…Continuous quantum measurements can be understood as the result of a sequence of infinitesimally weak measurements and are natural in physical settings in which the system-measurement device coupling is weak [36][37][38]. As such, and in parallel to QSL, they have given rise to advances in parameter estimation [39][40][41][42][43][44][45][46][47][48], quantum control [49][50][51][52][53][54][55], and foundations of physics [36,[56][57][58]. The ability to experimentally measure and manipulate individual quantum trajectories in this scenario motivates our study.…”