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Europhysics Letters (EPL)

Quantum thermometry based on interferometric power

Hongying Yang, Qiang Zheng, Ping Yue, Qi‐Jun Zhi

Published May 1, 2024• 4 citations
Publisher

Abstract

Abstract In the field of quantum thermometry, usually temperature is estimated by the framework of quantum metrology. In this work, an alternative approach to quantum thermometry is suggested, based on interferometric power (IP). IP is defined as the worst-case quantum Fisher information in a double-channel interferometer. Specifically, the time evolution of the IP for a two-qubit state as a probe contacting with a finite-temperature bath is considered. The IP dynamics of the probe with three kinds of initial states ( i.e. , entangled, separable, and mixed) strongly depend on the bath temperature. The dynamical evolution of IP would be measured experimentally, considering that the IP is a measurable quantity in the experiment. Thus, the IP dynamics can be adopted to extract the value of the bath temperature directly. In this sense, the IP could be exploited as a quantum thermometer.

DOI
10.1209/0295-5075/ad3c2f

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Abstract In the field of quantum thermometry, usually temperature is estimated by the framework of quantum metrology. In this work, an alternative approach to quantum thermometry is suggested, based on interferometric power (IP). IP is defined as the worst-case quantum Fisher information in a double-channel interferometer. Specifically, the time evolution of the IP for a two-qubit state as a probe contacting with a finite-temperature bath is considered. The IP dynamics of the probe with three kinds of initial states ( i.e. , entangled, separable, and mixed) strongly depend on the bath temperature. The dynamical evolution of IP would be measured experimentally, considering that the IP is a measurable quantity in the experiment. Thus, the IP dynamics can be adopted to extract the value of the bath temperature directly. In this sense, the IP could be exploited as a quantum thermometer.
Abstract We address the dephasing dynamics of the quantum Fisher information for the process of quantum thermometry with probes coupled to squeezed thermal baths via the nondemolition interaction. We also calculate the upper bound for the parameter estimation and investigate how the optimal estimation is affected by the initial conditions and decoherence, particularly the squeezing parameters. Moreover, the feasibility of the optimal measurement of the temperature is discussed in detail. Then, the results are generalized for entangled probes and the multi-qubit scenarios for probing the temperature are analysed. Our results show that the squeezing can decrease the number of channel uses for optimal thermometry. Comparing different schemes for multi-qubit estimation, we find that an increase in the number of the qubits, interacting with the channel, does not necessarily vary the precision of estimating the temperature. Besides, we discuss the enhancement of the quantum thermometry using the parallel strategy and starting from the W state.
The interferometric power of a bipartite quantum state quantifies the precision, measured by quantum Fisher information, that such a state enables for the estimation of a parameter embedded in a unitary dynamics applied to one subsystem only, in the worst-case scenario where a full knowledge of the generator of the dynamics is not available a priori. For finite-dimensional systems, this quantity was proven to be a faithful measure of quantum correlations beyond entanglement. Here we extend the notion of interferometric power to the technologically relevant setting of optical interferometry with continuous-variable probes. By restricting to Gaussian local dynamics, we obtain a closed formula for the interferometric power of all two-mode Gaussian states. We identify separable and entangled Gaussian states which maximize the interferometric power at fixed mean photon number of the probes and discuss the associated metrological scaling. At fixed entanglement of the probes, highly thermalized states can guarantee considerably larger precision than pure two-mode squeezed states.
The metrological limits of thermometry operated in nonequilibrium dynamical regimes are analyzed. We consider a finite-dimensional quantum system, employed as a quantum thermometer, in contact with a thermal bath inducing Markovian thermalization dynamics. The quantum thermometer is initialized in a generic quantum state, possibly including quantum coherence with respect to the Hamiltonian basis. We prove that the precision of the thermometer, quantified by the Quantum Fisher Information, is enhanced by the quantum coherence in its initial state. We analytically show this in the specific case of qubit thermometers for which the maximization of the Quantum Fisher Information occurs at a finite time during the transient thermalization dynamics. Such a finite-time precision enhancement can be better than the precision that is achieved asymptotically.
Interferometric power, based on the minimal quantum Fisher information in a black-box interferometer, can be used to measure general quantum correlation in a bipartite system. This paper explores the interferometric power of a two-qubit system in a common bath. It is found that, for an initially separable state, the interferometric power of the system can be produced with the time evolution, even subject to the dephasing environment. Moreover, it is asymmetric with respect to the local evolution implementing on one subsystem or another. Our result would be useful to quantum information processing beyond entanglement, especially in one-sided device-independent task.
Abstract High-precision low-temperature thermometry is a challenge for experimental quantum physics and quantum sensing. Here we consider a thermometer modeled by a dynamically-controlled multilevel quantum probe in contact with a bath. Dynamical control in the form of periodic modulation of the energy-level spacings of the quantum probe can dramatically increase the maximum accuracy bound of low-temperatures estimation, by maximizing the relevant quantum Fisher information. As opposed to the diverging relative error bound at low temperatures in conventional quantum thermometry, periodic modulation of the probe allows for low-temperature thermometry with temperature-independent relative error bound. The proposed approach may find diverse applications related to precise probing of the temperature of many-body quantum systems in condensed matter and ultracold gases, as well as in different branches of quantum metrology beyond thermometry, for example in precise probing of different Hamiltonian parameters in many-body quantum critical systems.
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the heat capacity when global measurements are performed on the system. We prove that if technical or practical limitations restrict our capabilities to local probing, the highest achievable accuracy to temperature estimation reduces to a sort of mesoscopic version of the heat capacity. Adopting a more practical perspective, we also discuss the relevance of qubit systems as optimal quantum thermometers, in order to retrieve the temperature, or to discriminate between two temperatures, characterizing a thermal reservoir. We show that quantum coherence and entanglement in a probe system can facilitate faster, or more accurate measurements of temperature. While not surprising given this has been demonstrated in phase estimation, temperature is not a conventional quantum observable, therefore these results extend the theory of parameter estimation to measurement of non-Hamiltonian quantities. Finally we point out the advantages brought by a less standard estimation technique based on sequential measurements, when applied to quantum thermometry.