Improved entanglement entropy estimates from filtered bitstring probabilities

Using the bitstring probabilities of ground states of bipartitioned ladders of Rydberg atoms, we calculate the mutual information which is a lower bound on the corresponding bipartite von Neumann quantum entanglement entropy $S^{vN}_A$. We show that in many cases, these lower bounds can be improved by removing the bitstrings with a probability lower than some value $p_{min}$ and renormalizing the remaining probabilities (filtering). Surprisingly, in some cases, as we increase $p_{min}$ the filtered mutual information tends to plateaus at values very close to $S^{vN}_A$ over some range of $p_{min}$. We consider various sizes, lattice spacings and bipartitions. Our numerical investigation suggest that the filtered mutual information obtained with samples having just a few thousand bitstrings can provide reasonably close estimates of $S^{vN}_A$. We briefly discuss practical implementations with the QuEra's Aquila device.