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Shadow tomography aims to build a classical description of a quantum statefrom a sequence of simple random measurements. Physical observables are thenreconstructed from the resulting classical shadow. Shadow protocols which usesingle-body random measurements are simple to implement and capture few-bodyobservables efficiently, but do not apply to systems with fundamental numberconservation laws, such as ultracold atoms. We address this shortcoming byproposing and analyzing a new local shadow protocol adapted to such systems.The "All-Pairs" protocol requires one layer of two-body gates and only$\textrm{poly}(V)$ samples to reconstruct arbitrary few body observables.Moreover, by exploiting the permutation symmetry of the protocol, we derive alinear time post-processing algorithm. We provide a proof-of-principlereference implementation and demonstrate the reconstruction of 2- and 4-pointfunctions in a paired Luttinger liquid of hardcore bosons.

Efficient Local Classical Shadow Tomography with Number Conservation