  How entangled is a randomly chosen bipartite stabilizer state? We show that
if the number of qubits each party holds is large the state will be close to
maximally entangled with probability exponentially close to one. We provide a
similar tight characterization of the entanglement present in the maximally
mixed state of a randomly chosen stabilizer code. Finally, we show that
typically very few GHZ states can be extracted from a random multipartite
stabilizer state via local unitary operations. Our main tool is a new
concentration inequality which bounds deviations from the mean of random
variables which are naturally defined on the Clifford group.
