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We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples.
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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, $$ Θ\left( \frac{dr}{\varepsilon^2} \max\left\{1,\frac r{\sqrt t}\right\} \right)$$ samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive....
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.10514v1 · Indexed about 2 hours ago