Tensor Products

1. Feb 4, 2009

Kreizhn

1. The problem statement, all variables and given/known data

Given that $\Gamma(\rho_A) = \displaystyle \sum_k A_k \rho_A(0) A_k^\dagger$, I need to show that if $\rho_{AB} (0)$ is a positive map, then $\rho_{AB}(t) = \Gamma\otimes 1_B ( \rho_{AB}(0) )$ is also a positive map.

2. Relevant equations

3. The attempt at a solution
This doesn't seem like it should be very hard, I'm just not very comfortable with tensor products. I'm not sure how this should be expanded out, and so if anyone could help, it would be appreciated.