Abstract The cutoff frequency is one of the crucial parameters that characterize the environment. In this paper, we estimate the cutoff frequency of the Ohmic spectral density by applying the π-pulse sequences (both equidistant and optimized) to a quantum probe coupled to a bosonic environment. To demonstrate the precision of cutoff frequency estimation, we theoretically derive the quantum Fisher information (QFI) and quantum signal-to-noise ratio (QSNR) across sub-Ohmic, Ohmic, and super-Ohmic environments, and investigate their behaviors through numerical examples. The results indicate that, compared to the equidistant π-pulse sequence, the optimized π-pulse sequence significantly shortens the time to reach maximum QFI while enhancing the precision of cutoff frequency estimation, particularly in deep sub-Ohmic and deep super-Ohmic environments.
We investigate the effect of the initial probe-environment correlations in estimating the cutoff frequency which is one of the crucial parameters characterizing the environment of a quantum system. The two-qubit probe, referred to as a probe constructed by two qubits, is prepared in the product state and allowed to interact with the environment. Under the initial probe-environment correlations, we derive the analytic quantum Fisher information (QFI) and the corresponding quantum signal-to-noise ratio (QSNR), which quantify the estimation accuracy of the cutoff frequency. By comparing the QFI and QSNR with the initial probe-environment correlations to those without correlations, it shows that the initial probe-environment correlations can be used to improve the accuracy of estimating the cutoff frequency in the estimation scheme of two-qubit probes.
We investigate the quantum sensing performance of a dephasing qubit as a probe in Ohmic environments, characterized by the coupling strength
η, the Ohmicity parameter
s, and the cutoff frequency
ωc to be estimated. The performance is quantified by the dimensionless quantum signal-to-noise ratio
Q. We show that the evolution of
Q with the scaled time
ωct is independent of
ωc, and peaks at an optimal time
topt, yielding optimal sensitivity
Qopt. We analyze how
Qopt depends on
η,
s and the temperature
T. Our results demonstrate that, for any Ohmic environment, provided that
ωctopt≪1,
Qopt always reaches the upper bound:
Qmax=0.648 at zero temperature, and consistently attains
Qmax/4 at high temperatures. Remarkably, we find that increasing the scaled temperature
T/ωc can enhance
Qopt by nearly two orders of magnitude compared to its zero-temperature counterpart for certain Ohmic environments. Our work reveals that temperature can serve as a resource to enhance sensing precision, as it accelerates the encoding of the cutoff frequency information into the probe state, thereby enabling optimal measurement within a short time window.
AbstractQuantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.
Abstract Quantum probing is the art of exploiting simple quantum systems interacting with a complex environment to extract precise information about some environmental parameters, e.g. the temperature of the environment or its spectral density. Here we analyze the performance of a single-qubit probe in characterizing Ohmic bosonic environments at thermal equilibrium. In particular, we analyze the effects of tuning the interaction Hamiltonian between the probe and the environment, going beyond the traditional paradigm of pure dephasing. In the weak-coupling and short-time regime, we address the dynamics of the probe analytically, whereas numerical simulations are employed in the strong coupling and long-time regime. We then evaluate the quantum Fisher information for the estimation of the cutoff frequency and the temperature of the environment. Our results provide clear evidence that pure dephasing is not optimal, unless we focus attention to short times. In particular, we found several working regimes where the presence of a transverse interaction improves the maximum attainable precision, i.e. it increases the quantum Fisher information. We also explore the role of the initial state of the probe and of the probe characteristic frequency in determining the estimation precision, thus providing quantitative guidelines to design optimized detection to characterize bosonic environments at the quantum level.
We propose an approach to implement a supersensitive estimation of the key parameters of the Ohmic-family spectral density with coherent spin states as the quantum sensor. This method can dramatically improve the estimation precision of the reservoir coupling strength as well as the cutoff frequency of the spectral density, by using both the number of spins
N and encoding time
t as effective resources. The quantum Fisher information indicates that the estimation sensitivity of the spectral density can surpass the shot-noise limit for all the sub-Ohmic, Ohmic, and super-Ohmic reservoirs. In particular, for super-Ohmic reservoirs, the precision can achieve a scaling $\ensuremath{\propto}1/(Nt)$. We also present the measurement scheme which can saturate the quantum Cram\'er-Rao bound.
Abstract We investigate the effect of the initial probe-environment correlations in estimating environment parameters. The probe constructed by two qubits, i.e. the two-qubit probe, is coupled with separate bosonic reservoirs and prepared in the product state. With the initial probe-environment correlations, we derive the analytic quantum Fisher information (QFI) and the corresponding quantum signal-to-noise ratio (QSNR) to quantify the estimation accuracy of environment parameters. The QFI and the QSNR increase when estimating cut-off frequency, coupling strength, and temperature, respectively, demonstrating that the initial probe-environment correlations can be used to improve the accuracy of estimating the environment parameters in the estimation scheme of two-qubit probes.