Negative off-diagonal elements in density matrix?

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SUMMARY

Negative off-diagonal elements in a density matrix are valid, as demonstrated by the density matrix for the state (up - down). In this context, diagonal elements represent probabilities, while all symmetric matrices can be diagonalized using a unitary transformation. This confirms that negative off-diagonal elements do not invalidate the density matrix's properties.

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I have a quick question. I've been trying to search for an answer, but I'm probably looking in the wrong places.

Is it valid to have negative off-diagonal elements in a density matrix?

Thanks!
 
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Sure, just take the density matrix for the state (up - down).
 
Of course.

In diagonal form you can interpret the diagonal elements as probabilities. But in addition you know that all symmetric matrices can be diagonalized via a unitary transformation.
 

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