In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper, we investigate two SU(2) TPT models and propose the singular behavior of the quantum metric tensor around the TPT point as a tool for the simultaneous optimal estimation of multiple parameters. We find that the proposed TPT sensing protocol can achieve the same metrology performance as the quantum-control-enhanced one. Moreover, the probe state of the TPT sensing protocol is only the ground state of the Hamiltonian rather than the entangled state required in the control-enhanced one. In addition, an adaptive multiparameter estimation strategy is developed for updating the estimated values until the desired quantum Cram\'er-Rao bound is approached. Our work reinforces the connection between quantum multiparameter estimation and topology physics, with potential inspiration for quantum critical metrology.
In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper, we investigate two SU(2) TPT models and propose the singular behavior of the quantum metric tensor around the TPT point as a tool for the simultaneous optimal estimation of multiple parameters. We find that the proposed TPT sensing protocol can achieve the same metrology performance as the quantum-control-enhanced one. Moreover, the probe state of the TPT sensing protocol is only the ground state of the Hamiltonian rather than the entangled state required in the control-enhanced one. In addition, an adaptive multiparameter estimation strategy is developed for updating the estimated values until the desired quantum Cram'er-Rao bound is approached. Our work reinforces the connection between quantum multiparameter estimation and topology physics, with potential inspiration for quantum critical metrology.
In the SU(2) dynamics, it is especially significant to achieve a simultaneous optimal multiparameter estimation but it is very difficult. Evolution on SU(N) dynamics is a research method to explore simultaneous multiparameter estimation with the quantum network. As the highly entangled states, graph state, is an intrinsical quantum resource for quantum metrology. For n-qubit graph state, we propose a simultaneous multiparameter estimation scheme that investigates evolution in SU(N) dynamics. For single-parameter estimation, the precision limit beyond the Heisenberg limit in the higher dimension spin of SU(2). We consider two scenarios where the Hamiltonian operator is commutation and non-commutation respectively and verify that the global estimation precision is higher than the local estimation precision. In the parameter limit condition, the precision of parameter estimation for the simultaneous estimation of each parameter is equal to the precision of the singleparameter estimation. In addition, we find a precision-enhancement scheme that depends on the dynamics SU(N). The smaller the N for the dynamics evolution, the higher the precision of the parameter estimation. Finally, we prove that the graph state is the optimal state of quantum metrology, a set of optimal measurement basic can be found, and the precision limit of multiparameter estimation can attain the quantum Cramér-Rao bound.
Periodically driven systems provide a powerful platform for quantum multiparameter estimation. Constructing a static effective Hamiltonian in a proper rotating frame is commonly employed to assess the attainable precision. However, such an approach becomes nonfeasible for more general time-periodically driven systems. To tackle this dilemma, we develop a quantum multiparameter estimation strategy in the Floquet theory framework. The contributions of Floquet eigenmodes, quasienergies, and multi-photon processes to the quantum Fisher information matrix and measurement incompatibility are determined, respectively. Moreover, this approach is applied to a ring-shaped Rashba spin-orbit interferometer model exhibiting the topological phase transition (TPT). In the vicinity of the TPT boundary, we reveal a pronounced enhancement in the estimation precision of multiple parameters with the Heisenberg limit scaling and even higher. Meanwhile, the measurement incompatibility vanishes in an oscillatory manner, and the stroboscopic projective measurement enables the highest estimation precision achievable. This work provides a complete Floquet picture for time-dependent critical quantum multiparameter estimation.
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.
In a ubiquitous SU(2) dynamics, achieving the simultaneous optimal estimation of multiple parameters is significant but difficult. Using quantum control to optimize this SU(2) coding unitary evolution is one of solutions. We propose a method, characterized by the nested cross products of the coefficient vector X of SU(2) generators and its partial derivative ${\ensuremath{\partial}}_{\ensuremath{\ell}}\mathbf{X}$, to investigate the control-enhanced quantum multiparameter estimation. Our work reveals that quantum control is not always functional in improving the estimation precision, which depends on the characterization of an SU(2) dynamics with respect to the objective parameter. This characterization is quantified by the angle ${\ensuremath{\alpha}}_{\ensuremath{\ell}}$ between X and ${\ensuremath{\partial}}_{\ensuremath{\ell}}\mathbf{X}$. For an SU(2) dynamics featured by ${\ensuremath{\alpha}}_{\ensuremath{\ell}}=\ensuremath{\pi}/2$, the promotion of the estimation precision can get the most benefits from the controls. When ${\ensuremath{\alpha}}_{\ensuremath{\ell}}$ gradually closes to 0 or $\ensuremath{\pi}$, the precision promotion contributed to by quantum control correspondingly becomes inconspicuous. Until a dynamics with ${\ensuremath{\alpha}}_{\ensuremath{\ell}}=0$ or $\ensuremath{\pi}$, quantum control completely loses its advantage. In addition, we find a set of conditions restricting the simultaneous optimal estimation of all the parameters, but fortunately, which can be removed by using a maximally entangled two-qubit state as the probe state and adding an ancillary channel into the configuration. Lastly, a spin-1/2 system is taken as an example to verify the above-mentioned conclusions. Our proposal sufficiently exhibits the hallmark of control-enhancement in fulfilling the multiparameter estimation mission, and it is applicable to an arbitrary SU(2) parametrization process.
Level crossings, where two quantum energy levels intersect, are ubiquitous in quantum systems and play a central role in controlling quantum dynamics. In this study, we establish a framework that connects these level crossing structures to the ultimate precision limits of quantum metrology. By analyzing a Hamiltonian with the level crossings structure, we identify the conditions under which multiple parameters can be estimated simultaneously with maximal sensitivity near the level crossing point. We then construct a resource efficient sensing protocol based on unitary quench dynamics and Bayesian estimation, enabling high precision, low cost parameter estimation without requiring entanglement or complex control. We present a protocol whose estimation precision saturates the Holevo Cramer Rao bound, the tightest achievable precision bound in multi parameter estimation. Using the two level model and the two spin Ising model as illustrative examples, we demonstrate how the protocol can be applied to a system with level crossing Hamiltonian structure. Our findings reveal that level crossings serve as universal operating points for precision quantum metrology, offering a simple and scalable path toward practical multi parameter sensing across diverse quantum platforms.
Abstract In quantum metrology, achieving optimal simultaneous multiparameter estimation is of great significance but remains highly challenging. The research approach involving evolution on dynamics provides a framework to investigate simultaneous multiparameter estimation within graph states. For single‐parameter estimation, it is observed that the precision limit exceeds the Heisenberg limit in higher‐dimensional spin systems. For multiparameter estimation, two scenarios are considered: one with commutative Hamiltonian operators and another with non‐commutative Hamiltonian operators. The results demonstrate that the global estimation precision exceeds the local estimation precision. Under the conditions of parameter limit, the precision of parameter estimation for simultaneously estimating each parameter is equal to that of single‐parameter estimation. Furthermore, a precision‐enhancement scheme has been identified that depends on the dynamics of . The smaller the value of in the dynamic evolution, the higher the precision of the parameter estimation. Finally, it is demonstrated that graph states serve as optimal states in quantum metrology. A set of optimal measurement bases is also identified, and it is illustrated that the precision limit of multiparameter estimation can attain the quantum Cramér‐Rao bound.