Adaptive quantum state tomography improves accuracy quadratically

We introduce a simple protocol for adaptive quantum state tomography, which reduces the worst-case infidelity between the estimate and the true state from $O(N^{-1/2})$ to $O(N^{-1})$. It uses a single adaptation step and just one extra measurement setting. In a linear optical qubit experiment, we demonstrate a full order of magnitude reduction in infidelity (from $0.1$ to $0.01$) for a modest number of samples ($N=3\times10^4$).

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