Does measurement violate unitarity?

1. Feb 15, 2016

hideelo

I am taking my first semester of QM so excuse my question if it is way off mark, totally wrong, or very well known.

As I understand it, one of the postulates of QM are that states evolve unitarily, a consequence (but not THE defining feature) of unitary transformations is that they are invertible.

Consider some system in state ∑ αii > where |Ψi > are the eigenstates of some observable. Now if I measure my system, then after the measurement the state will be |Ψi > i.e. it will be entirely in that state in which I found it to be.

If I am correct, then we can represent this by the transformation (1/αi)Pi where Pi is the projection onto the ith eigenstate and (1/αi) rescales it so that <Ψ|Ψ> = 1.

The problem is that projections arent unitary. In general they arent even invertable. So am I wrong about measurements violating unitarity? Is unitary transformations not a strict requirement?

Thanks

2. Feb 15, 2016

Staff: Mentor

3. Feb 15, 2016

Staff: Mentor

Sure.

However when entangled with other systems that can break untitary evolution by turning a pure state into an effective mixed state.

Thanks
Bill