Title: Symmetries and asymptotics of port-based teleportation
|Affiliation:||University of Waterloo|
|Zoom:||Please email Emma Watson|
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 in representation-theoretic terms, as first exhibited by Studzinski et al. One of their main results is a formula for the entanglement fidelity of the "standard PBT protocol" based on EPR pairs and the pretty good measurement. I will give a simplified proof of this result using classical results from Schur-Weyl duality and the Pieri rule. Time permitting, I will also explain how to infer the asymptotic behavior of the entanglement fidelity for fixed local dimension and a large number of ports using an interesting connection between the asymptotics of the Schur-Weyl distribution and random matrix theory.
This talk is partly based on unpublished work and the paper arXiv:1809.10751 (to appear in Communications in Mathematical Physics), which is joint work with M. Christandl, C. Majenz, G. Smith, F. Speelman, and M. Walter.