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Suppose $H_i$ are traceless $d\times d$ Hermitians, $X_i$ are Standard normal distribution for $1\leq i\leq d^2$.

We would like to bound the following expectation on the trace norm

$\mathbb{E}|\sum_{1\leq i\leq d^2}\frac{\sum_{j=1}^mx_{i,j}}{m}H_i|_{tr},$

where $x_{i,j}$ are iid sample of $X_i$.

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