Improved entanglement entropy estimates from filtered bitstring probabilities

TL;DR

This paper introduces a filtering method to improve estimates of quantum entanglement entropy from bitstring probabilities in Rydberg atom systems, achieving accurate results with fewer samples.

Contribution

It proposes a heuristic filtering technique to enhance entanglement entropy bounds from bitstring data, reducing the number of samples needed for accurate estimates.

Findings

Filtering improves entropy estimates significantly.

Few thousand samples suffice for close approximation.

Method is applicable to practical quantum devices.

Abstract

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.