Reconstructing Variance/Std Dev in Gate-Based Circuit Cutting with Finite Number of Shots

[conformalfield]

Hello,

I'm working with gate-based circuit cutting, specifically following tutorials like "Gate Cutting to Reduce Circuit Width." I've seen that reconstruct_expectation_values from qiskit_addon_cutting can be used to combine expectation values from sub-experiments.

My question is: How can one reconstruct the variance (or standard deviation) for the original observable when performing shot-based experiments (on simulators or real devices)?

Unlike the ideal, shotless case, shot-based simulations will yield variances from each sub-experiment due to the finite number of shots. What's the recommended approach or available functionality within qiskit_addon_cutting to combine these individual variances into a total variance for the original, uncut observable?