IQUIST seminar: "Optimality of the pretty good measurement for port-based teleportation"

Speaker Felix Leditzky, University of Waterloo
Date: 12/1/2020
Time: 11 a.m.
Event Contact: Becky McDuffee
Sponsor: IQUIST
Event Type: Seminar/Symposium

Port-based teleportation (PBT) is a protocol in which Alice teleports an unknown quantum state to Bob using measurements on a shared entangled multipartite state called the port state and forward classical communication. We give an explicit proof that the so-called pretty good measurement, or square-root measurement, is optimal for the PBT protocol with independent copies of maximally entangled states as the port state. We then show that the very same measurement remains optimal even when the port state is optimized to yield the best possible PBT protocol. Hence, there is one particular pretty good measurement achieving the optimal performance in both cases. The following well-known facts are key ingredients in the proofs of these results: (i) the natural symmetries of PBT, leading to a description in terms of representation-theoretic data; (ii) the operational equivalence of PBT with certain state discrimination problems, which allows us to employ duality of the associated semidefinite programs. Along the way, we rederive the representation-theoretic formulas for the performance of PBT protocols proved in [Studzinski et al., 2017] and [Mozrzymas et al., 2018] using only standard techniques from the representation theory of the unitary and symmetric groups. Providing a simplified derivation of these beautiful formulas is one of the main goals of this work.

Based on arXiv:2008.11194


Password: IQUIST

To request disability-related accommodations for this event, please contact the person listed above, or the unit hosting the event.

Event Mailing List

Receive Illinois Physics events weekly in your inbox.


Remove me!