Constraints on QCD-based equation of state of quark stars from neutron star maximum mass, radius, and tidal deformability observations

(Abridged) Neutron stars (NSs), the densest known objects composed of matter, provide a unique laboratory to probe whether strange quark matter is the true ground state of matter. We investigate the parameter space of the equation of state of strange stars using a quantum chromodynamics (QCD)-informed model. The parameters - related to the energy density difference between quark matter and the QCD vacuum, the strength of strong interactions, and the gap parameter for color superconductivity - are sampled via quasi-random Latin hypercube sampling to ensure uniform coverage. To constrain them, we incorporate observational data on the maximum mass of NSs (from binary and merger systems), the radii of $1.4$ M$_{\odot}$ NSs (from gravitational wave and electromagnetic observations), and tidal deformabilities (from GW170817). Our results show that quark strong interactions play a key role, requiring at least a $20\%$ deviation from the free-quark limit. We also find that color superconductivity is relevant, with the gap parameter reaching up to $\sim 84$ MeV for a strange quark mass of $100$ MeV. The surface-to-vacuum energy density jump lies in the range $(1.1-1.3)$ $\rho_{\rm{sat}}$, where $\rho_{\rm{sat}} \simeq 2.7 \times 10^{14}$ g cm$^{-3}$. Observational constraints also imply that a $1.4$ M$_{\odot}$ quark star has a radius of $(11.5-12.3)$ km and tidal deformability between $670$ and $970$. These are consistent with the low mass and radius inferred for the compact object XMMU J173203.3-344518. Our results provide useful inputs for future studies on quark and hybrid stars, including their tidal properties, thermal evolution, quasi-normal modes, and ellipticities.