Hyperon-antihyperon system in electron-positron annihilation as quantum probes for temperature estimation with local and global dephasing

Abstract

We investigate quantum thermometry in Ohmic-type reservoirs using two-qubit probes within an exactly solvable pure-dephasing framework. By analyzing the individual variance associated with temperature estimation, we identify optimal regimes governed by the Ohmicity parameter $s$, the deviation angle $\theta$, and the decay coefficients $\alpha$ and $\beta$, thereby determining the conditions that minimize estimation errors. The Quantum Fisher Information (QFI) exhibits pronounced maxima at finite interaction times, especially in sub-Ohmic and Ohmic environments at low temperatures, whereas super-Ohmic reservoirs flatten the QFI peak and shift the optimal sensitivity toward higher temperatures. Consistently, the quantum signal-to-noise ratio (QSNR) is suppressed at low temperatures, increases with thermal excitation, and saturates in the high-temperature regime, where the influence of spectral details becomes negligible. A comparative study of mutual and local estimation strategies shows that common-bath configurations, particularly for ${\Sigma }^{+}$ and ${\Sigma }^0$ probes, outperform local baths at short interaction times due to bath-induced correlations, while local environments become advantageous at longer times. The analysis further reveals finite optimal values of both the interaction time $t_{\mathrm{opt}}$ and the temperature $T_{\mathrm{opt}}$, as well as a strong reduction of the variance with increasing measurement number in the low-temperature regime. In addition, our study of hyperon-antihyperon channels ($\Lambda$, ${\Sigma }^{+}$, ${\Sigma }^0$, ${\Xi }^{-}$, ${\Xi }^0$) shows that entanglement and quantum discord remain remarkably robust over broad angular domains, whereas steering and Bell nonlocality are confined to narrower regions. Overall, the interplay between spectral structure, particle-dependent parameters, and estimation strategy provides valuable ...