A stabilizer state for a stabilizer set S for a system of qubits can be written as ρ=12n∑gϵSg . If we take a bipartition A-B of our system and partial trace over A, we get ρB=12nB∑gϵSBg where SB is the subet of elements in S which are non-zero when traced over A . Entanglement Entropy of ρB is proven as equal to nB−|SB| where |SB| is the rank of SB or the size of its minimal generating set. Its trivial to see the first part of the result nB but the complete result nB−|SB| requires to prove that Tr[12nB∑gϵSBg(log∑gϵSBg)]=|SB| . Is there an easy way to prove this ? If it helps, I found this result here http://arxiv.org/abs/quant-ph/0406168
This post imported from StackExchange at 2015-10-14 16:58 (UTC), posted by SE-user user56199