# Quantum entanglement and measurement operator

1. Feb 26, 2012

### superiority

1. The problem statement, all variables and given/known data
A system in a state $\frac{1}{\sqrt{2}}(\left<\phi\right| + \left<\psi\right|)$ undergoes an interaction with a second system (which is initially in $\left<\alpha\right|$) and ands up in an entangled state $\frac{1}{\sqrt{2}}\left(\left\langle\phi\right| \otimes \left\langle\alpha\right| + \left\langle\psi\right|\otimes \left\langle\beta\right|\right)$. Find a unitary operator that will perform that interaction/measurement.

The respective states in each space are orthonormal, and φ and ψ form a complete basis.

2. Relevant equations
I assume the linearity of tensor products is relevant. Other than that, I'm really not sure what.

3. The attempt at a solution
I don't know nearly enough about entanglement or unitary operators here. An entangled state means one that isn't separable, I know. A unitary operator U satisfies U*U = UU* = I. From there... I don't know.

Last edited by a moderator: Feb 26, 2012