Tight Lower Bounds for State Tomography with Limited Entanglement
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 blocks. The lower bound already applies in a small neighborhood of any state whose smallest eigen...
| Authors | Ufuk Keskin, Jason Luo, Mahbod Majid et al. |
|---|---|
| Primary category | quant-ph |
| Published | 4 September 2026 |
| Last updated at source | 4 September 2026 |
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