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 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.
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.
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.
Small, controllable quantum systems, known as quantum probes, have been proposed to estimate various parameters characterizing complex systems such as the environments of quantum systems. These probes, prepared in some initial state, are allowed to interact with their environment, and subsequent measurements reveal information about different quantities characterizing the environment, such as the system-environment coupling strength, the cutoff frequency, and the temperature. These estimates have generally been made by considering only the way that the probe undergoes decoherence. However, we show that information about the environment is also imprinted on the probe via the probe and environment correlations that exist before the probe state preparation. This information can then be used to improve our estimates for any environment. We apply this general result to the particular case of a two-level system probe undergoing pure dephasing, due to a harmonic-oscillator environment, to show that a drastic increase in the quantum Fisher information, and hence the precision of our estimates, can indeed be obtained. We also consider applying periodic control pulses to the probe to show that with a combination of the two---the effect of the control pulses as well as the initial correlations---the quantum Fisher information can be increased by orders of magnitude.
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.
We study how a second qubit can improve the estimation of spin-environment parameters when only one of the two qubits is measured. Both qubits are coupled to a common spin bath through the exactly solvable central-spin model, in which populations and coherences both evolve. Because the bath operator coupled to the qubits commutes with the bath Hamiltonian, the environment induces no effective interaction between the qubits. Without initial correlations or direct inter-qubit coupling, the two-qubit probe therefore performs exactly like a single qubit. When initial system-environment correlations are included, preparing the second qubit reshapes the environment statistics in a parameter-dependent way, and the measured qubit reads out this imprint. This improves the quantum Fisher information (QFI) for the coupling strength by factors of 3-4 relative to a correlated single-qubit probe, and by more than an order of magnitude relative to an uncorrelated one. For temperature estimation, the improvement reaches a factor of about 8. A direct Ising coupling does not help by itself, but the advantage persists in its presence. We also derive the classical Fisher information for arbitrary projective measurements and identify the measurement that saturates the QFI, which in general lies out of the equatorial plane of the Bloch sphere.
We demonstrate how using two qubits can drastically improve the estimation of environment parameters compared to using only a single qubit. The two qubits are coupled to a common harmonic oscillator environment, and the properties of the environment are imprinted upon the dynamics of the two qubits. The reduced density matrix of only one of these qubits contains a decoherence factor and an additional factor taking into account the indirect interaction induced between the qubits due to the interaction with their common environment. This additional factor can drastically improve the estimation of the environment parameters, as quantified by the quantum Fisher information. In particular, we investigate the estimation of the cutoff frequency, the coupling strength, and the temperature using our two-qubit scheme compared to simply using a single qubit. We find that the precision of the estimates can be improved by orders of magnitude.