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

TL;DR

The paper develops a multiparameter quantum estimation framework for the process e^+e^- -> J/ψ -> B B̄ at BESIII, leveraging the Quantum Fisher Information Matrix and Symmetric Logarithmic Derivative to bound precision in estimating the scattering angle φ and the vector charmonium decay parameter α_ψ. Using a vectorization-based approach, it derives the QFIM in both noiseless and noisy (correlated dephasing) settings and compares simultaneous versus individual parameter estimation strategies. In the noiseless case, simultaneous estimation can outperform independent estimation, with a strong dependence of precision on φ and α_ψ, and an optimal regime near φ = π/2 and α_ψ = 1. When environmental noise is included, Markovian and non-Markovian dynamics reveal memory effects that influence the time evolution of estimation variances, with non-Markovian regimes offering memory-supported stability and preserving the superiority of joint estimation. These results establish the QFIM as a practical tool for assessing ultimate precision limits in open quantum systems relevant to high-energy processes and hyperon decay parameters.

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.

Figures (11)

• Figure 1: (a) The Feynman diagram illustrating the annihilation process $e^{+}e^{-}\to \text{B}\bar{\text{B}}$. (b) The orientation of the coordinate axes $\{\hat{x}, \hat{y}, \hat{z}\}$, established in the mutual rest frame of the $\text{B}$ and $\bar{\text{B}}$ pair.
• Figure 2: (a) Plot of the minimum variances of the simultaneous estimates $\mathrm{Var}(\varphi)_{\min}$ in the $e^+e^- \to J/\psi \to \text{B} \bar{\text{B}}$ process as a function of the scattering angle $\varphi$ in theoretical case: $\alpha_{\psi} \in [0,1]$, $\beta_{\psi}=0.4$ and $\gamma_{\psi}=0$. (b) Plot of the minimum variances of the simultaneous estimates $\mathrm{Var}(\varphi)_{\min}$ for the $e^+e^- \to J/\psi \to \text{B} \bar{\text{B}}$ process, with $\text{B} \bar{\text{B}}\equiv (\Lambda\bar{\Lambda}, \Xi^0\bar{\Xi}^0, \Xi^-\bar{\Xi}^+)$ channels, incorporating the experimental values provided in Table \ref{['t1']}.
• Figure 3: (a) Plot of the minimum variances of the simultaneous estimates $\mathrm{Var}(\varphi)_{\min}$ in the $e^+e^- \to J/\psi \to \text{B} \bar{\text{B}}$ process as a function of the scattering angle $\varphi$ in theoretical case: $\alpha_{\psi} \in [-1,0]$, $\beta_{\psi}=0.4$ and $\gamma_{\psi}=0$. (b) Plot of the minimum variances of the simultaneous estimates $\mathrm{Var}(\varphi)_{\min}$ for the $e^+e^- \to J/\psi \to \text{B} \bar{\text{B}}$ process, with $\text{B} \bar{\text{B}}\equiv (\Lambda\bar{\Lambda}, \Xi^0\bar{\Xi}^0, \Xi^-\bar{\Xi}^+)$ channels, incorporating the experimental values provided in Table \ref{['t1']}.
• Figure 4: (a) Plot of the minimal variance of the simultaneous estimation $\mathrm{Var}(\alpha_{\psi})_{\min}$ of the decay parameter $\alpha_{\psi}$ as a function of the $\alpha_{\psi}$ for various value of the angle $\varphi$. (b) Plot of the minimal variance for the individual estimation of the decay parameter $\alpha_{\psi}$ as a function of the $\alpha_{\psi}$ for various value of the $\varphi$, in the high-energy limit ($\beta_{\psi}=\gamma_{\psi}=0$).
• Figure 5: Plot of the minimum variance of Individual estimates ${\rm Var}(\varphi)^{\rm Ind}_{\rm min}$ of the scattering angle $\varphi$ with $\beta_{\psi}=0.4$ and $\gamma_{\psi}=0$, for (a) $\alpha_{\psi}\in[0,1]$, and (b) $\alpha_{\psi}\in[-1,0]$.