We investigate multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature $T$ and detuning $Λ$. By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.
We investigate multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature T and detuning Λ. By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.
We investigate multiparameter quantum estimation in a Raman-coupled two-qubit system at thermal equilibrium. Analytical expressions for the quantum Fisher information matrix are derived to characterize the simultaneous estimation of the temperature and Raman coupling strength. The corresponding quantum Cramér--Rao bounds are obtained and compared with those of individual estimation strategies. Our results reveal optimal operating regimes determined by the interplay between thermal fluctuations and coherent interactions. In particular, quantum thermometry exhibits a well-defined optimal temperature window, whereas the estimation of the Raman coupling strength is significantly enhanced in the low-temperature and weak-coupling regime. We further show that simultaneous estimation can outperform independent estimation within appropriate parameter regions, highlighting the advantages of multiparameter quantum metrology. These results provide analytical insights into the ultimate precision limits of Raman-coupled two-qubit systems and identify promising operating regimes for quantum sensing and quantum thermometry.
The characterization of electric and magnetic dipole moments (EDM and MDM) in quantum systems is central to fundamental physics and quantum sensing. While EDM searches provide powerful probes of CP violation within and beyond the Standard Model, precise MDM estimation is crucial for high-precision magnetometry and the development of quantum sensors. In this work, we address the ultimate precision limits for separate and simultaneous estimation of both dipole moments in a generic two-level system coupled to electromagnetic fields. We analyze three classes of quantum probes/strategies: unitary and depolarizing dynamics, and thermal equilibrium states. For each, we derive the quantum Fisher information (matrix), identify optimal probes, and determine the ideal operating conditions, such as evolution times and temperatures, that maximize estimation precision. We further assess the compatibility and sloppiness of the statistical models, showing that orthogonal dipole moments configurations enable joint estimation of EDM and MDM, whereas parallel configurations are intrinsically sloppy, permitting only the estimation of a single parameter combination. Our results provide a unified metrological framework for estimation schemes ranging from neutron EDM searches to molecular magnetometry, and highlight the distinct roles of coherence, noise, and thermalization in multiparameter quantum sensing of dipole moments.
In this work, we investigate the relationship between quantum coherence and multiparameter quantum estimation in a graphene-based system. We focus on the estimation of two relevant physical parameters, namely the temperature T and the wave vector kx, and analyze how their variations affect both quantum coherence and the achievable metrological precision. The minimum variances associated with the estimation process are evaluated through the quantum Cramér--Rao bound within both simultaneous and independent estimation schemes. Our results show that quantum coherence is enhanced in the low-temperature regime and around kx=0, while it decreases progressively as either the temperature or the wave vector increases. However, the regions where coherence is maximal do not necessarily coincide with those of optimal estimation precision. In particular, the variance associated with temperature estimation exhibits a divergent behavior near T=0, indicating that the system becomes weakly sensitive to small temperature variations in this regime. By contrast, the estimation of the wave vector kx is more directly related to the coherence properties of the system, with improved precision obtained near kx=0. Furthermore, we introduce the ratio Γ to compare the total variances obtained from the independent and simultaneous estimation schemes. This quantity provides a useful measure of the relative difference between the two strategies when the parameters are estimated separately or jointly.
We present a quantum thermometric protocol for the estimation of multiple temperatures within the collisional model framework. Employing the formalism of multiparameter quantum metrology, we develop a systematic strategy to estimate the temperatures of several thermal reservoirs with minimal estimation error. We prove a necessary and sufficient condition for the singularity of the Fisher information matrix for a bi-parametrized qubit state. By using controlled rotations of ancillary systems between successive interaction stages, we eliminate parameter interdependencies, thereby rendering the quantum Fisher information matrix non-singular. Remarkably, we demonstrate that precision enhancement in the joint estimation of multiple temperatures can be achieved even in the absence of correlations among the ancillas, surpassing the corresponding thermal Fisher information limits. Exploiting correlations within the ancillary system yields additional enhancement of Fisher information. Finally, we identify the dimensionality of the ancillary systems as a key factor governing the efficiency of multiparameter temperature estimation.
Accurate simultaneous estimation of temperature and effective detuning is crucial for understanding, controlling, and optimizing optomechanical systems. Temperature characterizes the thermal state and mechanical properties, while detuning governs the light-motion interaction, influencing stability and enabling diverse quantum applications. Precise estimates of these parameters are therefore essential to exploit the full potential of such systems in high-precision metrology and the exploration of macroscopic quantum phenomena. In this work we investigate the simultaneous estimation of the effective detuning Δ and the mirror temperature T in a Fabry-Pérot cavity system, with a particular focus on the performance of heterodyne detection. Using analytical expressions for the quantum Fisher information matrices (QFIM) derived from the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD), we demonstrate that the quantum Cramér-Rao bound associated with the RLD is consistently lower than that based on the SLD, highlighting superior estimation precision. This gap between the SLD- and RLD-based bounds becomes especially pronounced in certain physical regimes, emphasizing the relevance of choosing the appropriate formalism in noncommutative estimation scenarios. From a physical perspective, the improved estimation performance stems from the fact that temperature directly influences thermal fluctuations in the mechanical mode, while the effective detuning modulates the strength of the optomechanical interaction, shaping the information exchange between optical and mechanical subsystems. We showed that using higher optical power, greater cavity decay rate, increased photon and phonon numbers, and reduced coupling strength improves the precision of both parameter estimates. These physical mechanisms affect the available quantum resources in the system—such as squeezing, entanglement, and state purity—which in turn determine the ultimate sensitivity achievable. Furthermore, our analysis shows that heterodyne detection can, under certain conditions, approach the ultimate precision set by the QFIM. Thus, a measurement strategy based on heterodyne detection could enable the efficient estimation of temperature, achieving performance close to that of ideal quantum-limited strategies.
Critical quantum metrology exploits the hypersensitivity of quantum systems near phase transitions to achieve enhanced precision in parameter estimation. While single-parameter estimation near critical points is well established, the simultaneous estimation of multiple parameters, which is essential for practical sensing applications, remains challenging. This difficulty arises from sloppiness, a phenomenon that typically renders the quantum Fisher information matrix (QFIM) singular or nearly singular. In this work, we demonstrate that multiparameter critical metrology is not only feasible but can also retain divergent precision scaling, provided one accepts a trade-off in the scaling exponent. Using the ground state of the single-cavity Dicke model (DM), we show that two Hamiltonian parameters can be simultaneously estimated with a scalar variance bound scaling as the square root of the critical parameter. This overcomes the inherent sloppiness by leveraging higher-order contributions to the QFIM. To recover the optimal quadratic scaling, we introduce the Dicke dimer (DD) with photon hopping. In this extended model, a triple point in the phase diagram enables the simultaneous closure of two excitation gaps, which effectively increases the rank of the QFIM and restores the ideal single-parameter scaling for specific parameter pairs. Furthermore, we extend our analysis to dissipative settings subject to photon loss. Finally, we establish a connection between the derived critical scalings and the fundamental state preparation time, providing a unified framework to operationally compare different sensing strategies. Our results demonstrate that critical quantum metrology can be made robust against dissipation and scalable to multiparameter scenarios, paving the way for practical quantum sensors operating near phase transitions.