  We provide alternative proofs of two recent Grothendieck theorems for jointly
completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko
(Invent. Math. 2002) and Haagerup and Musat (Invent. Math. 2008). Our proofs
are elementary and are inspired by the so-called embezzlement states in quantum
information theory. Moreover, our proofs lead to quantitative estimates.
