Asymptotic performance of portbased teleportation
Abstract
Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, portbased teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous nonlocal quantum computation and attacks on positionbased quantum cryptography. In this work, we determine the fundamental limit on the performance of PBT: for arbitrary fixed input dimension and a large number $N$ of ports, the error of the optimal protocol is proportional to the inverse square of $N$. We prove this by deriving an achievability bound, obtained by relating the corresponding optimization problem to the lowest Dirichlet eigenvalue of the Laplacian on the ordered simplex. We also give an improved converse bound of matching order in the number of ports. In addition, we determine the leadingorder asymptotics of PBT variants defined in terms of maximally entangled resource states. The proofs of these results rely on connecting recentlyderived representationtheoretic formulas to random matrix theory. Along the way, we refine a convergence result for the fluctuations of the SchurWeyl distribution by Johansson, which might be of independent interest.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.10751
 Bibcode:
 2018arXiv180910751C
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 68 pages, 4 figures