Improved entanglement entropy estimates from filtered bitstring probabilities of Rydberg simulators for lattice gauge theory

In recent years, arrays of Rydberg atoms have been used to build quantum simulators for lattice gauge theory.

In this context, the study of the entanglement entropy provides important information regarding critical points and continuum limits.

Recently, we found empirically that the mutual information associated with the bitstring probabilities of complementary subsets A and B of one-dimensional quantum chains, provide reasonably sharp lower bounds on the corresponding bi-partite von Neumann quantum entanglement entropy [1]. More recently, we found that hese bounds

can be sharpened by removing the bitstrings with a probability lower than some minimal value [2].

We discuss the asymptotic behavior of state occupations in the limit of small probabilities.

These observations were found for ladders of Rydberg atoms using numerical methods and analog simulations with Aquila.