Symmetries and asymptotics of port-based teleportation

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.