Is the trace of an outer product always equal to 1?

[kq6up]

Is the trace of an outer product of a normalized state eq. (psi) equal to 1?

Thanks,
Chris Maness

 

[atyy]

The most common outer product of a normalized state is with its dual. This outer product is called the density matrix. The density matrix formed from a pure state and its dual does have trace 1.

http://www.cs.berkeley.edu/~vazirani/f04quantum/notes/mixed.pdf
http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_9corr.pdf

 

[George Jones]

Is the trace of an outer product of a normalized state eq. (psi) equal to 1?

It would be good for you to calculate this.

Let $\left\{\left| \psi_i \right>\right\}$ be an orthonormal basis.

Steps:

1) express $\left| \psi \right>$ as an arbitrary linear combination of basis elements; 2) express the outer product in terms of this linear combination; 3) find the trace with respect to this basis.

You might need a few more hints.

 

[kq6up]

I think I have it, but my LaTeX editor is giving me fits with this half bra-ket stuff. I will post it after I install MacTex on my new computer.

That will be a while 2.2Gb later.

Regards,
Chris Maness

 

[dextercioby]

If you know the code, you can type LaTex here. We've got enabled through Mathjax.