My lecturer keeps telling me that if a density matrix describes a pure state then it must contain only one non-zero eigenvalue which is equal to one. However I can't see how this is true, particularly as I have seen a matrix [tex]\rho_A = \begin{pmatrix} 1/2 & - 1/2 \\ -1/2 & 1/2 \\ \end{pmatrix}[/tex] for which this is not true. He then clarified that if it was in "the diagonal basis" this was true. Can someone clarify this for me or show me a proof please?(adsbygoogle = window.adsbygoogle || []).push({});

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# Eigenvalues of a reduced density matrix

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