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Bianchi and Don\`{a} [1] have recently reported a proof to the varianceformula of von Neumann entropy, which was conjectured in [2] and firstly provedin [3]. The purpose of this short note is to show that, despite having adifferent starting point, the subsequent calculations (omitted in [1]) leadingto the result are essentially the same as in [3].

A note on Bianchi-Don\`a's proof to the variance formula of von Neumann entropy