Quantum steering and discord in hyperon-antihyperon system in electron-positron annihilation

TL;DR

The paper analyzes quantum steering and quantum discord in hyperon–antihyperon pairs produced in $e^+e^-$ annihilation, using an $X$-shaped two-qubit density operator derived from CP-symmetric spin correlations. It derives analytical expressions for steering via the CJWR three-setting inequality and for discord in rank-2 $X$ states, highlighting how EMFFs encoded in $\alpha_\psi$ and $\Delta\Phi$ shape all four correlation measures. A partial hierarchy among Bell nonlocality, steering, entanglement, and discord is observed, with EMFFs playing a key role and phase effects altering the relationships in special cases. The work also addresses locality loopholes and detector-induced decoherence, proposing ways to benchmark and correct for decoherence and suggesting how quantum correlations could serve as probes of hadron compositeness and the energy dependence of EMFFs in collider experiments.

Abstract

Hyperon-antihyperon pairs produced in high-energy electron-positron annihilation are promising systems for the study of quantum information properties. In this work, we make an analysis of two types of quantum correlations, the quantum steering and discord, in hyperon-antihyperon systems produced in electron-positron annihilation based on the $X$-shaped spin density matrix. The behaviors of these quantum correlations differ from those in elementary particle-antiparticle systems such as the top quark and tau lepton due to the polarization effect. The hierarchy of quantum correlations is examined and partially confirmed in hyperon-antihyperon systems: $ \textrm{Bell Nonlocality} \subset \textrm{Steering} \subset \textrm{Entanglement} \subset \text{Discord}$. The loopholes and quantum decoherence effect are also discussed in our work.

Figures (10)

• Figure 1: The quantity $\mathcal{F}_{3}[\rho_{Y\bar{Y}}]$ for the three-setting measurement as functions of $\cos\vartheta$ ($\vartheta$ is the scattering angle) in $e^{+}e^{-}\to J/\psi\to Y\bar{Y}$ with the black solid, blue dash-dotted, green dashed, red dotted and long yellow dash-dotted lines representing $Y=\Lambda$, $\Sigma^{+}$, $\Sigma^{0}$, $\Xi^{-}$ and $\Xi^{0}$ respectively. The black horizontal line is the steering bound $\mathcal{F}_{3}=1$. The CJWR inequality is violated iff $\mathcal{F}_{3}>1$.
• Figure 2: The quantum discord $\mathcal{D}\left[\rho_{Y\bar{Y}}\right]$ as functions of $\cos\vartheta$ ($\vartheta$ is the scattering angle) in $e^{+}e^{-}\to J/\psi\to Y\bar{Y}$ with $Y=\Lambda$, $\Sigma^{+,0}$ and $\Xi^{-,0}$ corresponding to curves in black solid, blue dash-dotted, green dashed, red dotted and long yellow dash-dotted lines respectively. The black horizontal line is $\mathcal{D}=0$.
• Figure 3: The results for the geometric quantum discord $2\mathcal{D}_{G}[\rho_{Y\bar{Y}}]$ as functions of $\cos\vartheta$ ($\vartheta$ is the scattering angle) in $e^{+}e^{-}\to J/\psi\to Y\bar{Y}$ with $Y=\Lambda$, $\Sigma^{+}$, $\Sigma^{0}$, $\Xi^{0}$ and $\Xi^{-}$ corresponding to black solid, blue dash-dotted, green dashed, red dotted and long yellow dash-dotted lines respectively. The black horizontal line is the zero geometric discord $2\mathcal{D}_{G}=0$.
• Figure 4: Four different types of quantum correlations as functions $\cos\vartheta$ ($\vartheta$ is the scattering angle) in $e^{+}e^{-}\to J/\psi\to Y\bar{Y}$. The five panels from (a) to (e) correspond to $\Lambda$, $\Sigma^{+}$, $\Sigma^{0}$, $\Xi^{-}$ and $\Xi^{0}$ respectively. The normalized Bell nonlocality (BN) $\mathscr{B}$ is shown in blue dot-dashed lines, the normalized steering $\mathscr{S}$ is shown in yellow dashed lines, the normalized entanglement $\mathscr{E}$ is shown in black solid lines, and the discord $\mathscr{D}$ is shown in red dotted lines.
• Figure 5: The quantum correlations for $\Xi^{0}\bar{\Xi}^{0}$ with $\Delta\Phi=0$. The subfigure shows the result in Fig. \ref{['fig:hierarchy']} (e) for comparison. The Bell nonlocality $\mathscr{B}$, the steering $\mathscr{S}$, the entanglement $\mathscr{E}$, and the discord $\mathscr{D}$ are shown in blue dot-dashed, yellow dashed, black solid, and red dotted lines respectively.