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.
