<p>The bulk-boundary correspondence, which establishes the relationship between bulk topological invariants and the number of protected edge states, has been both theoretically and experimentally verified. However, some recent theoretical studies have demonstrated the breakdown of bulk-boundary correspondence caused by specific symmetries where the entanglement spectrum, rather than the edge spectrum, could manifest the bulk topology more generally. Due to the difficulties in measuring this in physical systems, the bulk-entanglement spectrum correspondence has not yet been experimentally confirmed. Here, we report several one-dimensional and two-dimensional acoustic crystals in which we experimentally probe the nonlocal correlations with the fermion filling analog, thereby verifying the above correspondence. This work provides a useful platform to study the interplay among topological phases, symmetries, and the entanglement spectrum.</p>