Qubit-Qutrit Quantum Tomography of hadronic $Λφ$ and $ΛK^{\ast 0}$ 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 $Λ\barΛ$ production. Extending these studies to unequal-spin hadronic final states poses a fundamental challenge: the $6\times6$ density matrix of a qubit-qutrit system contains 35 independent spin parameters, but the decays of $ΛV$ pairs, with $V=φ$ or $K<sup>{*0}$, 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-$\tfrac{1}{2}\otimes1$ systems and establish exact criteria for entanglement certification from the \textit{incomplete} density matrix. Compared with the $Λ\barΛ$ system, QQQT of $Λφ$ and $ΛK<sup>{*0}$ 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.