Entanglement redistribution of hyperon-antihyperon pair via sequential decay

TL;DR

This work analyzes how quantum correlations in spin-entangled hyperon–antihyperon pairs produced in $e^+e^-$ annihilation evolve under sequential weak decays. Using a helicity-based spin-density-matrix formalism, the authors derive explicit SDMs for both mother and daughter systems and quantify correlations with concurrence, negativity, and quantum discord. They demonstrate entanglement redistribution across phase space, including regimes of autodistillation and regimes where entanglement decreases but quantum discord can grow, underscoring the distinct behavior of different nonclassical resources. The results reveal that transverse hyperon polarization and the relative production phase $\Delta\Phi$ critically influence the entanglement dynamics, with discord providing a robust indicator of quantum correlations beyond entanglement. These insights advance understanding of weak hadronic decays as a platform for probing quantum correlations in relativistic, high-energy environments, with potential implications for polarization control in collider processes.

Abstract

Hyperon-antihyperon pairs produced in high energy electron-positron annihilation constitute a naturally spin-entangled system in the high energy regime. Recently, a probabilistic amplification of entanglement, termed autodistillation, has been found in the daughter baryon-antibaryon pairs from hyperon decay and is constrained by an upper boundary. This work demonstrates that the quantum entanglement in this process may be accompanied by a decrease, constrained by a lower boundary, but will not be completely lost. Thus, the entanglement of these systems undergoes redistribution within the phase space during the sequential decays of hyperons, and an important role of hyperon polarization is highlighted. By using the explicit spin density matrix of baryon pairs, it is also found that quantumness of the system characterized by quantum discord always have the possibility to increase during decay processes, even when entanglement evaluated by concurrence and negativity does not increase.

Figures (8)

• Figure 1: Definitions of the helicity angles for $e^+e^- \to Y \bar{Y}$ and the sequential decay $Y \rightarrow \Lambda \pi$. The helicity angles of $\bar{Y} \rightarrow \bar{\Lambda} \pi$ defined in the same manner are omitted.
• Figure 2: Upper: Concurrence of $\Xi^{-}\bar{\Xi}^{+}$ (black line) and $\Lambda\bar{\Lambda}$ (light grey region between red and blue lines) in the $e^+e^-\to J/\psi \to \Xi^{-} (\to \Lambda \pi^-)~\bar{\Xi}^{+} (\to \bar{\Lambda}\pi^+)$ process. Lower: Concurrence for $e^+e^-\to J/\psi \to \Xi^{0} (\to \Lambda \pi^0)~\bar{\Xi}^{0} (\to \bar{\Lambda}\pi^0)$ process.
• Figure 3: Upper: Concurrence of $\Xi^{-}\bar{\Xi}^{+}$ (black line) and $\Lambda\bar{\Lambda}$ (light grey region between red and blue lines) in the $e^+e^-\to \psi(2S) \to \Xi^{-} (\to \Lambda \pi^-)~\bar{\Xi}^{+} (\to \bar{\Lambda}\pi^+)$ process. Lower: Concurrence for $e^+e^-\to \psi(2S) \to \Xi^{0} (\to \Lambda \pi^0)~\bar{\Xi}^{0} (\to \bar{\Lambda}\pi^0)$ process with black and red curves overlapping.
• Figure 4: Upper: Negativity of $\Xi^{-}\bar{\Xi}^{+}$ (black line) and $\Lambda\bar{\Lambda}$ (light grey region between red and blue lines) in the $e^+e^-\to J/\psi \to \Xi^{-} (\to \Lambda \pi^-)~\bar{\Xi}^{+} (\to \bar{\Lambda}\pi^+)$ process. Lower: Negativity for $e^+e^-\to J/\psi \to \Xi^{0} (\to \Lambda \pi^0)~\bar{\Xi}^{0} (\to \bar{\Lambda}\pi^0)$ process.
• Figure 5: Upper: Negativity of $\Xi^{-}\bar{\Xi}^{+}$ (black line) and $\Lambda\bar{\Lambda}$ (light grey region between red and blue lines) in the $e^+e^-\to \psi(2S) \to \Xi^{-} (\to \Lambda \pi^-)~\bar{\Xi}^{+} (\to \bar{\Lambda}\pi^+)$ process. Lower: Negativity for $e^+e^-\to \psi(2S) \to \Xi^{0} (\to \Lambda \pi^0)~\bar{\Xi}^{0} (\to \bar{\Lambda}\pi^0)$ process with black and red curves overlapping.