# can a maximally entangled state undergo unitary time evolution to another maximally entangled state?

#1
Mon, 04/06/2012 - 14:06

#### can a maximally entangled state undergo unitary time evolution to another maximally entangled state?

say for example a maximally entangled state |\psi_{AB}>=1/sqrt(2)(|00>+|11>) (at time t0) has to transform to another maximally entangled state |\phi_{AB}>=1/sqrt(2)(|01>+|10>) (at time t1) via unitary time evolution then at a certain time t0<t<t1 the entanglement content of the state(at time t ) will not be maximal if we consider the S(tr_{A}(\rho_{AB})) as our measure of entanglement. So can we have this process in which our physical resource (entanglement) is not only not conserved but also first decreases then increases in time ?

## I got the answer i guess. I

I got the answer i guess. I can always do a direct product of my maximally entangled state with a environment state and undergo unitary time evolution of this combined state. And then take partial trace over environment . Then this new state might have a higher or lower entanglement content depending on weather it takes in entanglement from the environment or flushes it out.