  We demonstrate how motional degrees of freedom in optical tweezers can be
used as quantum information carriers. To this end, we first implement a
species-agnostic cooling mechanism via conversion of motional excitations into
erasures - errors with a known location - reminiscent of Maxwell's demon
thought experiment. We find that this cooling mechanism fundamentally
outperforms idealized traditional sideband cooling, which we experimentally
demonstrate in specific scenarios. By coherently manipulating the motional
state, we perform mid-circuit readout and mid-circuit erasure detection of an
optical qubit via local shelving into motional superposition states. We finally
entangle the motion of two atoms in separate tweezers, and utilize this to
generate hyper-entanglement by preparing a simultaneous Bell state of motional
and optical qubits. This work shows how controlling motion enriches the toolbox
of quantum information processing with neutral atoms, and opens unique
prospects for metrology enhanced by mid-circuit readout and a large class of
quantum operations enabled via hyper-entanglement.
