Projected classical shadows reconstruct full quantum states with O(4^n) copies in general and O(2^n r) for rank-r states, matching optimal bounds, and use O(n^2) copies for matrix-product states.
Currently no known method for similarly reducing CS scaling exists
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Enhancing Quantum State Reconstruction with Structured Classical Shadows
Projected classical shadows reconstruct full quantum states with O(4^n) copies in general and O(2^n r) for rank-r states, matching optimal bounds, and use O(n^2) copies for matrix-product states.