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 $S_A^{\text{vN}}$. We show that in many cases these lower bounds can be improved by removing the bitstrings with a probability lower than some value $p_{\text{min}}$ 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 $S_A^{\text{vN}}$. 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 $S_A^{\text{vN}}$. We briefly discuss practical implementations with QuEra's Aquila device.

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• Entanglement entropy
• Quantum entanglement
• Quantum simulation
• Rydberg atoms & molecules