4
$\begingroup$

I came a cross a problem when leaning Quantum PCA. I know that a mixed state is an ensemble of several quantum states. But I wonder whether these states that make up for the mixed state are orthogonal. If not, under what condition they are? I'm glad if you could help me with this:)

$\endgroup$
0

1 Answer 1

5
$\begingroup$

The decomposition of a mixed state is not unique. So, in general, there are both orthogonal and non-orthogonal decompositions of the same state. However, note that there is always an orthogonal decomposition, just made up of a mixture of the eigenvectors of the density matrix. (As the density matrix is Hermitian, its eigenvectors are always orthogonal).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.