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- W4378942468 abstract "For quantum state tomography on rank-$r$ dimension-$d$ states, we show that $widetilde{O}(r^{.5}d^{1.5}/epsilon) leq widetilde{O}(d^2/epsilon)$ copies suffice for accuracy $epsilon$ with respect to (Bures) $chi^2$-divergence, and $widetilde{O}(rd/epsilon)$ copies suffice for accuracy $epsilon$ with respect to quantum relative entropy. The best previous bound was $widetilde{O}(rd/epsilon) leq widetilde{O}(d^2/epsilon)$ with respect to infidelity; our results are an improvement since [ text{infidelity} leq text{relative entropy} leq text{$chi^2$-divergence}.] For algorithms that are required to use single-copy measurements, we show that $widetilde{O}(r^{1.5} d^{1.5}/epsilon) leq widetilde{O}(d^3/epsilon)$ copies suffice for $chi^2$-divergence, and $widetilde{O}(r^{2} d/epsilon)$ suffice for relative entropy. Using this tomography algorithm, we show that $widetilde{O}(d^{2.5}/epsilon)$ copies of a $dtimes d$-dimensional bipartite state suffice to test if it has quantum mutual information 0 or at least $epsilon$. As a corollary, we also improve the best known sample complexity for the classical version of mutual information testing to $widetilde{O}(d/epsilon)$." @default.
- W4378942468 created "2023-06-01" @default.
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- W4378942468 date "2023-05-29" @default.
- W4378942468 modified "2023-09-28" @default.
- W4378942468 title "Quantum chi-squared tomography and mutual information testing" @default.
- W4378942468 doi "https://doi.org/10.48550/arxiv.2305.18519" @default.
- W4378942468 hasPublicationYear "2023" @default.
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