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SUMMARY:Asymptotic performance of port-based teleportation - Felix Leditzk
 y
DTSTART:20181115T141500Z
DTEND:20181115T151500Z
UID:TALK113164@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:Quantum teleportation is one of the fundamental building block
 s of quantum Shannon theory. While ordinary teleportation is simple and ef
 ficient\, port-based teleportation (PBT) enables applications such as univ
 ersal programmable quantum processors\, instantaneous non-local quantum co
 mputation and attacks on position-based quantum cryptography. In this work
 \, we determine the fundamental limit on the performance of PBT: for arbit
 rary fixed input dimension and a large number N of ports\, the error of th
 e optimal protocol is proportional to the inverse square of N. We prove th
 is by deriving an achievability bound\, obtained by relating the correspon
 ding optimization problem to the lowest Dirichlet eigenvalue of the Laplac
 ian on the ordered simplex. We also give an improved converse bound of mat
 ching order in the number of ports. In addition\, we determine the leading
 -order asymptotics of PBT variants defined in terms of maximally entangled
  resource states. The proofs of these results rely on connecting recently-
 derived representation-theoretic formulas to random matrix theory. Along t
 he way\, we refine a convergence result for the fluctuations of the Schur-
 Weyl distribution by Johansson\, which might be of independent interest.\n
 \nBased on arXiv:1809.10751\, joint work with M. Christandl\, C. Majenz\, 
 G. Smith\, F. Speelman\, and M. Walter.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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