Quantum force estimation in arbitrary non-Markovian Gaussian baths

Abstract

The force estimation problem in quantum metrology with arbitrary non-Markovian Gaussian bath is considered. No assumptions are made on the bath spectrum and coupling strength with the probe. Considering the natural global unitary evolution of both bath and probe and assuming initial global Gaussian states we are able to solve the main issues of any quantum metrological problem: the best achievable precision determined by the quantum Fisher information, the best initial state and the best measurement. Studying the short time behavior and comparing to regular Markovian dynamics we observe an increase of quantum Fisher information. We emphasize that this phenomenon is due to the ability to perform measurements below the correlation time of the bath, activating non-Markovian effects. This brings huge consequences for the sequential preparation-andmeasurement scenario as the quantum Fisher information becomes unbounded when the initial probe mean energy goes to infinity, whereas its Markovian counterpart remains bounded by a constant. The long time behavior shows the complexity and potential variety of non-Markovian effects, somewhere between the exponential decay characteristic of Markovian dynamics and the sinusoidal oscillations characteristic of resonant narrow bands.

Fundamental limits to frequency estimation: a comprehensive microscopic perspective

“…Also there the optimal asymptotic scaling of the error is also found to be the same for PC and NPC dynamics, going from the SQL for a semigroup to the Zeno limit for a linear increase of the dissipative rates. Such a transition for a PC evolution of a Gaussian system has been shown also in [103].…”

Optimal estimation of conjugate shifts in position and momentum by classically correlated probes and measurements

“…It presents a more feasible scheme for the practical estimation of quantum displacement [40][41][42], because using sets of differently squeezed states is more feasible and therefore cheaper [58] than the entangled [33, 35,39] or quantum non-Gaussian states [34]. We expect it can have a direct impact on sensing of mechanical, electric, magnetic and optical forces [36][37][38]. It also demonstrates that even in multi-parameter quantum estimation it is not necessary to simultaneously estimate all the parameters in each trial, and that mixed states, together with classically correlated measurements, can be optimal.…”

“…One essential task of quantum sensing is estimation of parameters of a small mechanical, electrical, magnetic, or optical force [36][37][38]. A particular scenario commonly studied in this context is the simultaneous estimation of the position and momentum -two parameters of quantum displacement acting on a state of harmonic oscillator [33][34][35]39].…”

Noncommutative phase-space effects in thermal diffusion of Gaussian states

“…The presence of oscillations in the fidelity during a thermalization process has been largely studied in the literature as been associated to an information backflow from the thermal environment to the system [39,40]. Non-Markovian effects is a current field of research with several applications in quantum information [41,42] and quantum thermodynamics [43,44], both in theoretical and experimental areas [45]. As we have mentioned above, quantum fidelity obeys a significant property, i. e., monotonicity [46],…”