Analyzing Probability Distributions and Entanglement in Quantum Many-Body Systems.

We study the bitstring distributions of adiabatically prepared vacuum states of Rydberg arrays designed to quantum simulate lattice gauge theory models (see talks by Z. Ozzello and Y.Meurice in the April meeting and by R. Parker and M. Asaduzzaman in the March meeting). We find that with only a few thousand measurement outcomes from a single copy of the many-body states considered in this project, one can obtain reliable estimates of the bipartite von Neumann entanglement entropy. Our approach builds on a refined treatment of mutual information, where quantum signatures appear most strongly in the dominant configurations of the computational basis. We apply this method to data from analog quantum devices implemented with Rubidium and Strontium atoms and compare their performance across several error metrics. We also examine the limitations imposed by finite sampling, noise modeling, measurement protocols, and readout fidelity, and report on notable behaviors observed in larger experimental systems where direct classical simulation becomes intractable. Finally, analysis of exact theoretical distributions reveals that cumulative probability distributions exhibit systematic trends that can help anticipate scaling behavior in systems beyond classical reach. Ongoing developments and updated findings will be presented at the meeting.