Fig. 1: Quantum teleportation protocols.
a Standard teleportation, where the message encoded by ψR is transmitted from the sender Alice to receiver Bob. The protocol is enabled by implementing Θ0, which involves a Bell measurement on ψR ⊗ ρAB followed by unitary operations on Bob’s system B; b Teleportation with embezzling catalyst, where Alice and Bob have an additional catalyst \({\tau }_{C{C}^{{\prime} }}\) undergoing a transformation \(\Lambda \in {{{\rm{LOCC}}}}(RAC:B{C}^{{\prime} })\) and coming back slightly changed. The state \({\tau }_{C{C}^{{\prime} }}\) assists in improving the performance of teleportation protocol. Alice holds the part above the dashed line and Bob holds the part below it.
