  In this work, we report first exact volume-entangled Einstein-Podolsky-Rosen
(EPR) type scar states hosted by PXP and related Hamiltonians corresponding to
various geometric configurations of Rydberg-blockaded atom systems, including
the most extensively studied ones such as the chain with periodic boundary
conditions (PBC) and square lattice. We start by introducing a new zero-energy
eigenstate of the PBC chain and proceed by generalizing it to a wide variety of
geometries and Hamiltonians. We point out the experimental relevance of such
states by providing a concrete and feasible protocol for their preparation on
near-term Rydberg quantum devices, which relies only on strictly local
measurements and evolution under native Hamiltonians. We also demonstrate the
utility of these states for the study of quantum dynamics by describing a
simple protocol for measuring infinite-temperature out-of-time-order correlator
(OTOC) functions.
