In an article recently published in the journal Entropy, researchers demonstrated that the precision of the quantum thermometer can be enhanced by the quantum coherence in its initial state following a nonequilibrium approach for quantum thermometry.
Study: Quantum Coherence Boosts Thermometer Precision. Image Credit: Production Perig/Shutterstock.com
Background
Quantum thermometry infers a thermal bath/thermal reservoir's temperature through coupling with a quantum system. To a particular extent, all measurement devices, including a thermometer, are invasive in the quantum regime.
Thus, thermometry's ultimate goal from an estimation perspective is to ascertain the circumstances in which the thermal bath's temperature can be effectively attained. This task can be achieved using the tools provided by quantum metrology, specifically by applying quantum Fisher information (QFI) to quantum thermometry.
Recently, global thermometry has been proposed for cases where no prior knowledge is available regarding thermalization dynamics or only a few/limited measurement records can be obtained. The advantage of this method lies in establishing the mean logarithmic error as a reliable measure of accuracy in quantum thermometry.
Moreover, the collisional quantum thermometry framework identifies the possibility of probing an environment's temperature using correlated qubits in a sequential setting. Until now, several studies have analyzed the application of quantum thermometry in different quantum platforms.
The Study
In this study, researchers analyzed the metrological limits of thermometry operated in non-equilibrium dynamical regimes. They considered a finite-dimensional quantum system, utilized as a quantum thermometer, in contact with a thermal bath inducing Markovian thermalization dynamics.
Additionally, they initialized the quantum thermometer in a generic quantum state, including quantum coherence concerning the Hamiltonian basis. Researchers assumed that the quantum computer asymptotically reached the thermal state ρβ = e-βH/Zβ, with H denoting the Hamiltonian of the thermometer, Zβ the corresponding partition function, and β the inverse temperature of the bath.
Then, they considered that the thermometer interacted weakly with the thermal bath to ensure that the thermalization dynamics could be described effectively by a Markovian master equation in Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. The thermometer's time-evolved state always encoded information regarding the temperature researchers aimed to infer, as the studied thermalization dynamics resulted in an asymptotic thermal state irrespective of the initial state.
Under these conditions, one approach to inferring the thermal bath's temperature involved waiting for the thermometer to fully thermalize and then reconstructing T from its measurement. However, the time required for the thermometer to thermalize could be very long, with the potential emergence of other error sources in a nanoscopic setting. These errors could disturb the thermometer state, spoiling the information on T.
In this work, a non-equilibrium approach was followed for quantum thermometry that depended on measuring the thermometer's time-dependent state while the thermalization was still active. The bath's temperature was reconstructed from these measurements. Researchers computed the QFI, which relied on the GKSL master equation's parameters, the thermometer's initial state, and time, to guide the inference of the temperature with the highest precision.
The QFI is a precise metric for evaluating the precision of quantum thermometry, as the uncertainty of the temperature estimate (reconstructed from the quantum thermometer's state measurements) is bounded from below by the QFI, according to the quantum Cramér-Rao bound. Therefore, this work aimed to optimize both the initial state of the thermometer and its transient thermalization dynamics to maximize the QFI.
Importance of this Work
Researchers successfully computed the QFI associated with a quantum thermometer in weak contact with a thermal bath and validated that the precision of the thermometer could be enhanced by the quantum coherence in its initial state.
Specifically, maximizing the QFI enabled the determination of the optimal time within the transient thermalization dynamics and the quantum thermometer's initial state such that the thermometry precision was enhanced.
The researchers also analytically demonstrated this in the specific case of qubit thermometers, showing that the QFI maximization occurs at a finite time during the transient thermalization dynamics. This finite-time precision enhancement could surpass the precision achieved asymptotically.
The presence of quantum coherence in the thermometer's state results in a higher state purity, allowing the state to be mapped unitarily to a diagonal density operator with elements corresponding to a lower effective temperature. This scenario suggests that the increase in the QFI reflects a cooling effect induced by quantum coherence, assuming constant purity.
In summary, this study showcases the enhancement of single-qubit thermometry by quantum coherence in non-equilibrium conditions. The findings pave the way for further experimental tests, provided there is an estimation algorithm available that can use the qubit thermometer's density operator to determine the estimated inverse temperature during the period when QFI is maximized.
Journal Reference
Frazão, G., Pezzutto, M., Omar, Y., Zambrini Cruzeiro, E., Gherardini, S. (2024). Coherence-Enhanced Single-Qubit Thermometry out of Equilibrium. Entropy, 26(7), 568. DOI: 10.3390/e26070568, https://www.mdpi.com/1099-4300/26/7/568
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