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

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 $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ 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 $\mathrm{\Lambda }V$ pairs, with $V=\phi$ 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 $\mathit{\text{incomplete}}$ density matrix. Compared with the $\mathrm{\Lambda }\bar{\mathrm{\Lambda }}$ system, QQQT of $\mathrm{\Lambda }\phi$ and $\mathrm{\Lambda }{K}^{\ast 0}$ 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.