Quantum probes for the cutoff frequency of Ohmic environments

Abstract

Quantum probing consists of suitably exploiting a simple, small, and controllable quantum system to characterize a larger and more complex system. Here, we address the estimation of the cutoff frequency of the Ohmic spectral density of a harmonic reservoir by quantum probes. To this aim, we address the use of single-qubit and two-qubit systems and different kinds of coupling with the bath of oscillators. We assess the estimation precision by the quantum Fisher information of the sole quantum probe as well as the corresponding quantum signal-to-noise ratio. We prove that, for most of the values of the Ohmicity parameter, a simple probe such as a single qubit is already optimal for the precise estimation of the cutoff frequency. Indeed for those values, upon considering a two-qubit probe either in a Bell or in separable state, we do not find improvement to the estimation precision. However, we also showed that there exist few conditions where employing two qubits in a Bell state interacting with a common bath is more suitable for precisely estimating the cutoff frequency.

Two-qubit quantum probes for the temperature of an Ohmic environment

“…The single-qubit case has already been described in previous works, dealing with the purely dephasing bath, related both to the estimation of temperature or other bath parameters [16][17][18][19]. Here we focus, under the same conditions, on the two-qubit probe scenario, which allows us to explore the role of quantum correlations and the number of qubits in inferring the temperature.…”

Quantum bath statistics tagging

“…where now S(χ) = (25) cosh(|χ|) + sinh(|χ|) cos(2φ) sinh(|χ|) sin(2φ) sinh(|χ|) sin(2φ) cosh(|χ|) − sinh(|χ|) cos(2φ) , the matrices S(χ) and S A (χ) being related via the transformation…”

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 ...…”