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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

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Is a probabilistic implementation of unitaries invertible?

Let $\{p_j\}_j$ be a set of probabilities, $\sum_j p_j = 1$, let $\{h_j\}_j$ be a set of $n \times n$ Hermitian matrices, and define $ad_h(A) $ be the adjoint. Define the following linear mapping $$ E …