Maximizing Information on the Environment by Dynamically Controlled Qubit Probes

Abstract

We explore the ability of a qubit probe to characterize unknown parameters of its environment. By resorting to quantum estimation theory, we analytically find the ultimate bound on the precision of estimating key parameters of a broad class of ubiquitous environmental noises ("baths") which the qubit may probe. These include the probe-bath coupling strength, the correlation time of generic bath spectra, the power laws governing these spectra, as well as their dephasing times T2. Our central result is that by optimizing the dynamical control on the probe under realistic constraints one may attain the maximal accuracy bound on the estimation of these parameters by the least number of measurements possible. Applications of this protocol that combines dynamical control and estimation theory tools to quantum sensing are illustrated for a nitrogen-vacancy center in diamond used as a probe.

Quantum Sensing of Noisy and Complex Systems under Dynamical Control

“…The QZE and AZE correspond to the suppression and enhancement, respectively, of the bath effects via control. Dynamical control methods based on the QZE are aimed at protecting the quantumness (coherence or entanglement) of the probe [45,63,64], but also at diagnosing the bath spectra [9,15,65] and transferring QI via noisy media [43,[66][67][68][69]. By contrast, AZE-based control is useful for fast, versatile and robust cooling of thermalized quantum systems [51][52][53]70,71].…”

“…We shall not be concerned with the probing of mechanical degrees of freedom (phonon modes) for which the most appropriate probes are harmonic oscillators, as in optomechanical setups [8]. The peculiarity of the approach we present here is that rather than try to maximize the signal-to-noise ratio (SNR) obtainable by the probe, we set out to analyze and extract information from the noise exerted by the system on the probe [9]. Namely, the spectrum of fluctuations may be a viable source of information concerning a noisy, complex system which we shall treat as a "bath", e.g., a large molecule, an aggregate of interacting spins, a liquid, or stray fields at diverse frequencies.…”

“…In Section 3 we show how noise spectra may be extracted using BOTOC by the qubit probe [10,11]. Section 4 is dedicated to optimized estimation of the noise parameters, with a focus on a qubit probe [9]. In Sections 5 and 6, we discuss the transfer of the noise information from the qubit probe to a storage qubit [34,35] or through a quantum channel [43], respectively, under control derived from BOTOC that optimizes the fidelity or duration of the transfer.…”

“…This, however, is a laborious and time-consuming undertaking. Instead, it may suffice to record only a few parameters of the noise that provide a distinct signature of the bath: the bath structure and the dynamics of the underlying processes (e.g., diffusion, collisions and thermal fluctuations [9,[14][15][16][17][18][19]). We show here that such tasks may be accomplished with high fidelity or success probability by subjecting the probe to an appropriate dynamical control that may turn a sub-optimal into a fully optimal probing/sensing process.…”

“…Namely, the spectrum of fluctuations may be a viable source of information concerning a noisy, complex system which we shall treat as a "bath", e.g., a large molecule, an aggregate of interacting spins, a liquid, or stray fields at diverse frequencies. This emerging area of research, nicknamed "noise spectroscopy" [9][10][11][12][13], requires a detailed consideration of the probing process, in which we schematically discern the following stages: change of the probe state under the influence of the noise and control; transfer and storage of this state or at least its partial information content to either a storage device or an information processor for processing or improving the sensing process; readout and analysis of the extracted information.…”