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arXiv:2601.12097

Probing multiparameter quantum estimation in the process $e^+e^-\to J/ψ\to \text{B}\bar{\text{B}}$ at BESIII

Elhabib Jaloum, Mohamed Amazioug

quant-phSubmitted Jan 17, 2026• Announced Jan 20, 2026• 0 citations
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Abstract

The quantum Fisher information matrix (QFIM) is the cornerstone of multiparameter quantum metrology. In this work, we investigate multiparameter quantum estimation in baryon-antibaryon (B bar-B) pairs produced via the e+ e- -> J/psi -> B bar-B process at the BESIII experiment, utilizing the symmetric logarithmic derivative (SLD) formalism. Moreover, the QFIM defines the quantum Cramer-Rao bound and dictates the choice of optimal probe states. We compare individual and simultaneous estimation strategies for two key physical parameters: the scattering angle phi and the decay parameter alpha_psi. The estimation variances are found to depend strongly on the explored region of the (phi, alpha_psi) parameter space and to display markedly different temporal dynamics. In general, higher true values of a parameter increase the system's sensitivity, thereby significantly reducing the associated variance. While both variances increase with evolution time, they do so at distinct rates, revealing parameter-dependent information loss driven by environmental decoherence. These findings demonstrate the utility of the QFIM framework for multiparameter quantum estimation in realistic open systems and provide new insights into the ultimate precision limits achievable for hyperon decay parameters.

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20 pages, 11 figures

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Probing multiparameter quantum estimation in the process e+e−→J/ψ→BBˉe^+e^-\to J/ψ\to \text{B}\bar{\text{B}}e+e−→J/ψ→BBˉ at BESIII
The quantum Fisher information matrix (QFIM) is the cornerstone of multiparameter quantum metrology. In this work, we investigate multiparameter quantum estimation in baryon-antibaryon (B bar-B) pairs produced via the e+ e- -> J/psi -> B bar-B process at the BESIII experiment, utilizing the symmetric logarithmic derivative (SLD) formalism. Moreover, the QFIM defines the quantum Cramer-Rao bound and dictates the choice of optimal probe states. We compare individual and simultaneous estimation strategies for two key physical parameters: the scattering angle phi and the decay parameter alpha_psi. The estimation variances are found to depend strongly on the explored region of the (phi, alpha_psi) parameter space and to display markedly different temporal dynamics. In general, higher true values of a parameter increase the system's sensitivity, thereby significantly reducing the associated variance. While both variances increase with evolution time, they do so at distinct rates, revealing parameter-dependent information loss driven by environmental decoherence. These findings demonstrate the utility of the QFIM framework for multiparameter quantum estimation in realistic open systems and provide new insights into the ultimate precision limits achievable for hyperon decay parameters.
The quantum Fisher information matrix (QFIM) is central to multiparameter quantum metrology, dictating the attainable sensitivity via the quantum Cramér-Rao bound. In this work, we investigate the ultimate precision limits for relativistic quantum thermometry in a bipartite system of uniformly accelerated Unruh-DeWitt detectors. Utilizing the symmetric logarithmic derivative (SLD) formalism within the QFIM framework, we analyze the individual and simultaneous estimation of the Unruh temperature TTT and the initial-state parameter Δ0Δ_0Δ0​. In the noiseless case, we demonstrate that these two parameters are quantum compatible, allowing the multiparameter quantum Cramér-Rao bound to be saturated without a loss of precision. We then examine the impact of environmental effects by comparing Markovian and non-Markovian dynamics. In the Markovian regime, dissipation leads to a monotonic degradation of estimation precision; conversely, non-Markovian memory effects induce temporal oscillations and transient precision enhancements due to information backflow. The robustness of the estimation protocols is further analyzed under correlated noisy channels, including amplitude damping, phase flip, and phase damping. We show that dissipative noise results in more significant precision loss than purely dephasing mechanisms, whereas classical correlations in the noise mitigate this degradation. Finally, we discuss the estimation of the detector energy-level spacing ωωω as a natural extension, highlighting its sensitivity to the environmental structure. Our results provide a unified framework for relativistic multiparameter quantum metrology within the context of open quantum systems.
Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of determining the minimum achievable estimation error is a central task of multiparameter quantum metrology. For estimating parameters encoded in pure quantum states, the ultimate limit is known, but is given by the solution of a non-trivial minimisation problem. We present a new expression for the achievable bound for two-parameter estimation with pure states that is considerably simpler. We also determine the optimal measurements, completing the problem of two-parameter estimation with pure state probes. To demonstrate the utility of our result, we determine the precision limit for estimating displacements using grid states.
Abstract Multiparameter quantum estimation theory aims to determine simultaneously the ultimate precision of all parameters contained in the state of a given quantum system. Determining this ultimate precision depends on the quantum Fisher information matrix (QFIM) which is essential to obtaining the quantum Cramér–Rao bound. This is the main motivation of this work which concerns the computation of the analytical expression of the QFIM. Inspired by the results reported in J. Phys. A: Math. Theor. 52 035304 (2019), the general formalism of the multiparameter quantum estimation theory of quantum Gaussian states in terms of their first and second moments is given. We give the analytical formulas of right logarithmic derivative and symmetric logarithmic derivative operators. Then we derive the general expressions of the corresponding quantum Fisher information matrices. We also derive an explicit expression of the condition which ensures the saturation of the quantum Cramér–Rao bound in estimating several parameters. Finally, we examine some examples to clarify the use of our results.
Abstract Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cramér–Rao bound in quantum parameter estimation. However, studies in recent years have revealed wide connections between QFIM and other aspects of quantum mechanics, including quantum thermodynamics, quantum phase transition, entanglement witness, quantum speed limit and non-Markovianity. These connections indicate that QFIM is more than a concept in quantum metrology, but rather a fundamental quantity in quantum mechanics. In this paper, we summarize the properties and existing calculation techniques of QFIM for various cases, and review the development of QFIM in some aspects of quantum mechanics apart from quantum metrology. On the other hand, as the main application of QFIM, the second part of this paper reviews the quantum multiparameter Cramér–Rao bound, its attainability condition and the associated optimal measurements. Moreover, recent developments in a few typical scenarios of quantum multiparameter estimation and the quantum advantages are also thoroughly discussed in this part.
We investigate the interplay between quantum correlations and multiparameter quantum estimation in top--antitop quark pair production through the gluon-fusion channel. Using the spin density matrix formalism, we construct an effective two-qubit quantum state governed by the relativistic parameters associated with the scattering process. Within the framework of quantum metrology, we derive the quantum Fisher information matrix for the simultaneous estimation of the relativistic velocity parameter and the production angle, and we analyze the corresponding quantum precision bounds. Our results reveal highly nontrivial estimation regimes strongly controlled by relativistic spin correlations and scattering geometry. We further characterize the produced state through the concurrence and demonstrate the existence of strong connections between entanglement structures and multiparameter estimation sensitivity. Finally, we discuss the experimental feasibility of probing these effects at the Large Hadron Collider through spin-correlation observables and reconstructed top--antitop density matrices. Our results identify top--antitop production as a unique relativistic platform for exploring quantum information theory and multiparameter quantum metrology in high-energy physics.
We investigate the ultimate precision achievable in Gaussian quantum metrology. We derive general analytical expressions for the quantum Fisher information matrix and for the measurement compatibility condition, ensuring asymptotic saturability of the quantum Cram\'er-Rao bound, for the estimation of multiple parameters encoded in multimode Gaussian states. We then apply our results to the joint estimation of a phase shift and two parameters characterizing Gaussian phase covariant noise in optical interferometry. In such a scheme, we show that two-mode displaced squeezed input probes with optimally tuned squeezing and displacement fulfill the measurement compatibility condition and enable the simultaneous estimation of all three parameters, with an advantage over individual estimation schemes that quickly rises with increasing mean energy of the probes.