  From an open system perspective non-Markovian effects due to a nearby bath or
neighbouring qubits are dynamically equivalent. However, there is a conceptual
distinction to account for: neighbouring qubits may be controlled. We combine
recent advances in non-Markovian quantum process tomography with the framework
of classical shadows to characterise spatiotemporal quantum correlations.
Observables here constitute operations applied to the system, where the free
operation is the maximally depolarising channel. Using this as a causal break,
we systematically erase causal pathways to narrow down the progenitors of
temporal correlations. We show that one application of this is to filter out
the effects of crosstalk and probe only non-Markovianity from an inaccessible
bath. It also provides a lens on spatiotemporally spreading correlated noise
throughout a lattice from common environments. We demonstrate both examples on
synthetic data. Owing to the scaling of classical shadows, we can erase
arbitrarily many neighbouring qubits at no extra cost. Our procedure is thus
efficient and amenable to systems even with all-to-all interactions.
