Extended Data Fig. 8: Benchmarking the interferometry measurement.

a, To benchmark our gate-based interferometry technique, we prepare variable single-particle pure states (by applying a variable-length resonant Raman pulse) and then reconfigure the system and apply the interferometry circuit on twin pairs. The interferometry circuit converts the anti-symmetric singlet state |Ψ⁻⟩ to the computational basis state |00⟩, while converting the symmetric triplet states to other computational states. We plot the resulting twin pair output states in the left panel. We rarely observe the |00⟩ state (1.95(2)% of measurements), with a measurement fidelity independent of the initial state. This low probability P₀₀ of observing |00⟩ corresponds to a high extracted single-particle purity of 2P₀₀ − 1 = 0.961(3) (right panel). We find this measurement to be a useful benchmark, as interferometry miscalibrations can result in significant state-dependence of the observed purity that would then compromise the validity of the many-body entanglement entropy measurement. b, Benchmarking the entanglement entropy measurement with Bell state arrays. (Top) Microstate populations during two-particle oscillations between |11⟩ and \(\frac{1}{\sqrt{2}}(|1r\rangle +|r1\rangle )\) under a Rydberg pulse of variable duration. Faint lines show measurement results in the {|1⟩, |r⟩} basis, and dark lines show results in the {|0⟩, |1⟩} basis after the coherent mapping process. (Bottom) Measured local and global purities by analyzing the number parity of observed |00⟩ twin pairs in each measurement. For this two-particle data we use a gap of 230 ns in the coherent mapping sequence as opposed to the 150-ns gap used in the many-body data.