This is probably my misunderstanding of the notation...(adsbygoogle = window.adsbygoogle || []).push({});

The definition of a density matrix is in the attached file. (Sorry, the latex editor is not rendering properly when I preview my post).

This definition is a sum over only one index 'j', which will invariably lead to a diagonal matrix. But the density matrix is often not diagonal, for instance a basic superposition (pure) state. What am I missing in this definition? Shouldn't it be over indices i and j, for instance, in a two dimensional system?

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# Notation question for density matrix

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