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). We propose a heuristic based on the change of the conditional entropy under filtering that very effectively improves the estimate of $S^{vN}_A$. 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 QuEra's Aquila device.