Appears in collection : 2017 - T3 - WS1 - Operator algebras and quantum information theory

Quantum teleportation and superdense coding are fundamental protocols in quantum information theory. They together describe the resource trade-off between quantum communication and classical communication when assisted with remote entanglement. In terms of operator spaces, teleportation and superdense coding are interpreted as that $S_1^d$ and $l_1^{d^2}$ are completely embedded into the matrix level of each other. In this talk, I will discuss the lifted embedding of their C_-envelopes--Brown algebra and free group C_-algebra. It gives strong connections between these two kinds of universal C*-algebras, and also has applications in quantum correlation sets. This is a joint work with Marius Junge.