- #1
ma18
- 93
- 1
Homework Statement
Consider the bipartite state:
|q> = a/sqrt (2) (|1_A 1_B> +|0_A 0_B>)+sqrt((1-a^2)/2) (|0_A 1_B>+|1_A 0_B>)
where a is between or equal to 0 and 1
a) compute the state of the subsystem p_b
b) compute the purity of p_b as a function of a
c) for what values of a is the purity of p_b at a minimum/maximum
d) Compute the entanglement entropy of the bipartite state, for what value of a is it at a min/max
The Attempt at a Solution
I have done a) and found p_b to be :
p_b = |q_b><q_b|
where |q_b> = (a+sqrt(1-a^2))/sqrt(2) (|0_B>+|1_B>)
the computation for this is long and I don't want to replicate it here...
b)
I simply applied:
p (0_B,0_B) = <0_B|p_b|0_b> for the 4 combinations of |0_b> and |1_b> and got the matrix, then taking the trace of this for the diagonal terms I get 1/2 and 1/2 so the purity was equal to 1 and thus not dependent on a
c) It is unrelated
d) I know that the equation is
S (p_AB) = S (Tr_B p_AB)
but I don't know how to proceed from here
Any help such as how to proceed or checking my previous steps would be greatly appreciated!