Qubit-Qutrit Quantum Tomography of hadronic $\Lambda \varphi$ and $\Lambda K^{\ast 0}$ systems

Abstract

Quantum-information observables have emerged in recent years as new tools in nuclear and particle physics, from entanglement in top-quark pairs to spin correlations in $\Lambda \bar{\Lambda }$ production. Extending these studies to unequal-spin hadronic final states poses a fundamental challenge: the $6\times 6$ density matrix of a qubit-qutrit system contains 35 independent spin parameters, but the decays of $\Lambda V$ pairs, with $V=\varphi$ or $K^{\ast 0}$, provide access to only 23 due to the hidden vector polarization from the strong decay. In this Letter, we formulate a qubit-qutrit quantum tomography (QQQT) technique for these spin-$\frac{1}{2}\otimes 1$ systems and establish exact criteria for entanglement certification from the \textit{incomplete} density matrix. Compared with the $\Lambda \bar{\Lambda }$ system, QQQT of $\Lambda \varphi$ and $\Lambda K^{\ast 0}$ provides a new probe of nonperturbative QCD hadronization, enabling a direct comparison of the spin evolution of entangled quark pairs produced from the vacuum as they hadronize into a baryon or a vector meson.

Comments: A short letter with 4 pages, two figures, one table, and an Appendix