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Chinese Physics B

Environmental parameter estimation with the two-level atom probes

Mengmeng Luo, Wenxiao Liu, Yuetao Chen, Shangbin Han, Shaoyan Gao

Published Nov 4, 2021• 3 citations
Publisher

Abstract

A novel scheme is proposed to estimate three environmental parameters, the detuning, the temperature and the squeezing strength with one-qubit or two-qubit probes. Quantum Fisher information and the fidelity of the atom probes are calculated. When the detuning between the frequency of cavity field and the atomic transition frequency is estimated, the dynamics of quantum Fisher information shows oscillatory and rising behaviors. To estimate the temperature of the thermal reservoir, the one-qubit probe with the superposition initial state is more favorable than the two-qubit probe with the entangled initial state. When the squeezing strength of the squeezed vacuum reservoir is estimated, we find that the estimation precision is significantly improved by utilizing the two-qubit probe with the maximal entangled initial state. Our work provides a potential application in the open quantum system and quantum information processing.

DOI
10.1088/1674-1056/ac364f

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A novel scheme is proposed to estimate three environmental parameters, the detuning, the temperature and the squeezing strength with one-qubit or two-qubit probes. Quantum Fisher information and the fidelity of the atom probes are calculated. When the detuning between the frequency of cavity field and the atomic transition frequency is estimated, the dynamics of quantum Fisher information shows oscillatory and rising behaviors. To estimate the temperature of the thermal reservoir, the one-qubit probe with the superposition initial state is more favorable than the two-qubit probe with the entangled initial state. When the squeezing strength of the squeezed vacuum reservoir is estimated, we find that the estimation precision is significantly improved by utilizing the two-qubit probe with the maximal entangled initial state. Our work provides a potential application in the open quantum system and quantum information processing.
A scheme is proposed to estimate the system and environmental parameter, the detuning, temperature and the squeezing strength with a high precision by the two-level atom system. It hasn't been reported that the squeezing strength estimation through quantum Fisher information. We find entangled state and optimal superposition state are beneficial for parameter estimation with one-qubit probe by calculating quantum Fisher information and fidelity. And the fidelity between initial and final states of the atom can be improved via the two-qubit probe. Moreover, the phenomenon of quantum Fisher information return occurs when the detuning or the temperature is estimated. Our work provides a basis for precision measurement technology and quantum information processing.
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.
We address in detail the process of parameter estimation for an n-qubit system dissipating into a cavity in which the qubits are coupled to the single-mode cavity field via coupling constant g which should be estimated. In addition, the cavity field interacts with an external field considered as a set of continuum harmonic oscillators. We analyse the behaviour of the quantum Fisher information (QFI) for both weak and strong coupling regimes. In particular, we show that in strong coupling regime, the memory effects are dominant, leading to an oscillatory variation in the dynamics of the QFI and consequently information flowing from the environment to the quantum system. We show that when the number of the qubits or the coupling strength rises, the oscillations, signs of non-Markovian evolution of the QFI, increase. This indicates that in the strong-coupling regime, increasing the size of the system or the coupling strength remarkably enhances the reversed flow of information. Moreover, we find that it is possible to retard the QFI loss during the time evolution and therefore enhance the estimation of the parameter using a cavity with a larger decay rate factor. Furthermore, analysing the dynamics of the QFI and negativity of the probe state, we reveal a close relationship between the entanglement of probes and their capability for estimating the parameter. It is shown that in order to perform a better estimation of the parameter, we should avoid measuring when the entanglement between the probes is maximized.
We study the behavior of quantum Fisher information for a qubit probe that is interacting with a squeezed thermal environment. We analyzed the effect of squeezing parameters on the dynamics of quantum Fisher information which affects the optimal precision of the estimation parameter. We show that the squeezed field may offer a significant role in the precise measurement of the parameter cut-off frequency which is linked to the environment correlation time. Our results may be useful in quantum metrology, communication, and quantum estimation processes.
Abstract We study the impact of quantum correlations existing within the system-environment thermal equilibrium state while estimating the parameters of the spin reservoir. By employing various physical situations of interest, we present results for the reservoir temperature and its coupling strength with the central two-level system. The central system (probe) interacts with the bunch of randomly oriented spin systems and attains a thermal equilibrium state. We consider a projective measurement which prepares the probe’s initial state, and then the global system (probe and reservoir) evolves unitarily. The reduced density operator encapsulates the information about the spin reservoir which can be extracted by doing measurements on the probe. The precision of such measurement is quantified by quantum Fisher information. We repeat this process if the probe-reservoir initial state is not correlated (product state). We compare the estimation results for both with and without the outturn of initial correlations. In the temperature estimation case, our results are promising as one can significantly improve the accuracy of the estimates by including the effect of initial correlations. A similar trend prevails in the case of coupling strength estimation especially at low temperatures.
In the present manuscript, we demonstrate the potential to control and enhance the accuracy of parameter estimation (P-E) in a two-level atom (TLA) immersed in a cavity field that interacts with another cavity. We investigate the dynamics of quantum Fisher information (FI), considering the influence of coupling strength between the two cavities and the detuning parameter. Our findings reveal that, in the case of a perfect cavity, a high quantum FI value can be maintained during the dynamics concerning the detuning and coupling strength parameters. The results indicate that with a proper choice of quantum model parameters, long-term protection of the FI can be achieved without being affected by decoherence.