We present a science case for the QUEST and SPI-QG experiment at Cardiff University as a probe of the ground state of gravitational entanglement. It is commonly assumed that the low energy limit of quantum gravity is uncontroversially described by a perturbative effective field theory of graviton modes. However, this framework presumes a classical, definite space-time as its background. This construction is mathematically inconsistent, both with the renormalization process of non-gravitational modes and with a holographic limit on the degrees of freedom of the background space-time. We argue that a correct treatment of the infrared limit of quantum gravity requires large scale entanglement in the background space-time itself. This should be thought of as the ground state of gravitational entanglement. While the community's pursuit of gravitational entanglement has focused on large coherent states of quantum matter dynamically coupling to measurable superpositions of geometry, this talk will make the case that in holographic models, even quantum superpositions of mass-energy in vacuum states may result in measurably large irreducible correlations in the background space-time. We present the latest updates in our research program to empirically probe such correlations of quantum space-time, connecting signatures in the CMB arising from primordial space-times to experimental data from state-of-the-art laser interferometers enhanced with novel quantum metrology under commissioning at Cardiff.