Lower bounds on entanglement entropy without twin copy

Journal Article · Thu Apr 24 00:00:00 EDT 2025 · Physical Review Research

DOI:https://doi.org/10.1103/PhysRevResearch.7.L022023· OSTI ID:2562717

Meurice, Yannick

We discuss the possibility of estimating experimentally the von Neumann entanglement entropy $S_A^{vN}$ of a symmetric bipartite quantum system $AB$ by using the basic measurement counts (bitstrings) for a single copy of a prepared state. Using exact diagonalization and analog simulations performed with the publicly available QuEra facilities for chains and ladders of Rydberg atoms, we calculate the Shannon entropy $S_{AB}^X$ associated with the bitstrings of adiabatically prepared ground states and the reduced entropies $S_A^X$ and $S_B^X$ obtained from the marginal probabilities in $A$ and $B$ . We then calculate the classical mutual information $I_{AB}^X=S_A^X+S_B^X-S_{AB}^X$ , which is a lower bound on $S_A^{vN}$ . We show that for a broad range of lattice spacing and detuning, $I_{AB}^X$ is typically 20% below $S_A^{vN}$ in regions where $S_A^{vN}$ is large and a less close bound in regions where $S_A^{vN}$ is low. We argue that this use of the easily available bitstrings provides a robust and efficient way to explore empirically the phase diagram of qubit-based quantum simulators and identify critical regions.

Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019139
• OSTI ID: 2562717
• Journal Information: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 2 Vol. 7; ISSN PPRHAI; ISSN 2643-1564
• Publisher: American Physical Society
• Country of Publication: United States
• Language: English