Abstract : We provide alternative proofs of two recent Grothendieck theorems for jointly completely bounded bilinear forms, originally due to Pisier and Shlyakhtenko (Grothendieck's theorem for operator spaces, \textit{Invent. Math.} \textbf{150}(2002), 185--217) and Haagerup and Musat (The Effros-Ruan conjecture for bilinear forms on ${C}^*$-algebras, \textit{Invent. Math.} \textbf{174}(2008), 139--163). Our proofs are elementary and are inspired by the so-called embezzlement states in quantum information theory. Moreover, our proofs lead to quantitative estimates.
