# I have been hanging on this problem for a long time without a solution

1. Jul 9, 2007

### dream_chaser

I have been hanging on this problem for a long time without a solution!!

Suppose we have a single qubit principal system ,interacting with a single qubit environment through the transformation
U=P0$$\otimes$$I+P1$$\otimes$$X
where X is the usual Pauli matrix (acting on the enviornment)and P0=|0><0| ,P1=|1><1| are projectors (acting on the system ).Give the quantum operation for this process ,in the operator-sum representation ,assuming the environment starts in the state |0>