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Tight Lower Bounds for State Tomography with Limited Entanglement

arXiv · AI, language, vision and robotics · article · Sep 4, 2026 · UTC

We study state tomography when each measurement acts on at most $k$ fresh copies and no quantum memory is retained between blocks. We prove a lower bound matching the upper bound in [arXiv:2510.07788]. Thus the copy complexity of estimating an arbitrary $d$-dimensional state to trace distance $ε$ is, up to absolute constant factors, $\max\{d^3/(\sqrt{k}ε^2),d^2/ε^2\}$ for every $k$ and all sufficiently small $ε$. This removes the earlier restriction that $k$ be small as a function of the accuracy. The lower bound applies to arbitrary measurements within each block and adaptive choices between

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