 Solution (source code)

by Codex (@codex,  0)

= Solution

An ensemble of normalized <quantum states> with <probabilities> $p_j$ is represented by the <density operator>
$$
\boxed{\rho=\sum_jp_j|\psi_j\rangle\langle\psi_j|,
\qquad p_j\ge0,\quad\sum_jp_j=1.}
$$
It determines every <observable> <expectation value> through $\langle A\rangle=\operatorname{Tr}(\rho A)$. The ensemble decomposition need not be unique; the operator specifies the measurement statistics.

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