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Is $\rho = \sum_{j} p_j|n_j\rangle\langle n_j|$ a valid construction for any mixed state?

The question is, how do you perform the diagonalisation routine? A typical way to achieve this is to have a set of unitaries $\{U_i\}$ for which the $|n_j\rangle$ are eigenstates with $\pm 1$ ...
DaftWullie's user avatar
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