Suppose we have two copies of Bell states +) which undergo the decoherence process and evolve into mixed states (also known as Werner states) given by Pw = Fv+) (+] + -[|v_) (v_| + |_) (0-|+|+) (0+|]. 1 F 3 where F is the entanglement fidelity. (a) Show how one entangled state of higher fidelity (F') could be obtained with two entangled states of lower fidelity (F) provided F > 1/2, where F' is given by F = F + (1-F) 9 - F + F(1 F) + (1 F) (b) One can carry out the above purification process N times and obtain the new fidelity F. Assume that the initial fidelity of two Bell states is 0.6. Plot how the improved fidelity varies with the number of purification steps up to 20 steps.