  Minimizing and understanding errors is critical for quantum science, both in
noisy intermediate scale quantum (NISQ) devices and for the quest towards
fault-tolerant quantum computation. Rydberg arrays have emerged as a prominent
platform in this context with impressive system sizes and proposals suggesting
how error-correction thresholds could be significantly improved by detecting
leakage errors with single-atom resolution, a form of erasure error conversion.
However, two-qubit entanglement fidelities in Rydberg atom arrays have lagged
behind competitors and this type of erasure conversion is yet to be realized
for matter-based qubits in general. Here we demonstrate both erasure conversion
and high-fidelity Bell state generation using a Rydberg quantum simulator. We
implement erasure conversion via fast imaging of alkaline-earth atoms, which
leaves atoms in a metastable state unperturbed and yields additional
information independent of the final qubit readout. When excising data with
observed erasure errors, we achieve a lower-bound for the Bell state generation
fidelity of ${\geq} 0.9971^{+10}_{-13}$, which improves to
${\geq}0.9985^{+7}_{-12}$ when correcting for remaining state preparation
errors. We further demonstrate erasure conversion in a quantum simulation
experiment for quasi-adiabatic preparation of long-range order across a quantum
phase transition, where we explicitly differentiate erasure conversion of
preparation and Rydberg decay errors. We unveil the otherwise hidden impact of
these errors on the simulation outcome by evaluating correlations between
erasures and the final readout as well as between erasures themselves. Our work
demonstrates the capability for Rydberg-based entanglement to reach fidelities
in the ${\sim} 0.999$ regime, with higher fidelities a question of technical
improvements, and shows how erasure conversion can be utilized in NISQ devices.
