Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. The original teleportation protocol is an exact protocol and amazingly simple, but it requires a non-trivial correction operation to make it work. Port-based teleportation (PBT) is an approximate variant of teleportation with a simple correction operation that renders the protocol unitarily covariant. This property enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based quantum cryptography. The natural symmetries of PBT allow for an elegant mathematical description of optimal protocols in representation-theoretic terms. I will explain these symmetries and show how to use Schur-Weyl duality to describe the asymptotics of optimal port-based teleportation protocols.
This talk is based on arXiv:1809.10751, joint work with M. Christandl, C. Majenz, G. Smith, F. Speelman, and M. Walter.
