Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements
We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknown state on $\mathbb{C}^d$ of rank at most $r$ to trace norm error $\varepsilon$ with constant success probability requires, and is achievable with, $$Θ\left(\frac{dr}{\varepsilon^2}\mathop{\mathrm{max}}\left\{1,\frac{r}{\sqrt{t}}\right\}\right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most $t$ samples improve the complexity of algorith...
| Authors | Ashwin Nayak, Xingyu Zhou |
|---|---|
| Primary category | quant-ph |
| Published | 9 September 2026 |
| Last updated at source | 5 October 2026 |
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