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CATEGORIES:CQIF Seminar
SUMMARY:Asymptotic performance of port-based teleportation
- Felix Leditzky
DTSTART;TZID=Europe/London:20181115T141500
DTEND;TZID=Europe/London:20181115T151500
UID:TALK113164AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/113164
DESCRIPTION:Quantum teleportation is one of the fundamental bu
ilding blocks of quantum Shannon theory. While ord
inary teleportation is simple and efficient\, port
-based teleportation (PBT) enables applications su
ch as universal programmable quantum processors\,
instantaneous non-local quantum computation and at
tacks on position-based quantum cryptography. In t
his work\, we determine the fundamental limit on t
he performance of PBT: for arbitrary fixed input d
imension and a large number N of ports\, the error
of the optimal protocol is proportional to the in
verse square of N. We prove this by deriving an ac
hievability bound\, obtained by relating the corre
sponding optimization problem to the lowest Dirich
let eigenvalue of the Laplacian on the ordered sim
plex. We also give an improved converse bound of m
atching order in the number of ports. In addition\
, we determine the leading-order asymptotics of PB
T variants defined in terms of maximally entangled
resource states. The proofs of these results rely
on connecting recently-derived representation-the
oretic formulas to random matrix theory. Along the
way\, we refine a convergence result for the fluc
tuations of the Schur-Weyl distribution by Johanss
on\, which might be of independent interest.\n\nBa
sed on arXiv:1809.10751\, joint work with M. Chris
tandl\, C. Majenz\, G. Smith\, F. Speelman\, and M
. Walter.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Johannes Bausch
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