Asymptotic Performance of Port-Based Teleportation

Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and atta...

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Bibliographic Details
Published in:Communications in mathematical physics 2021-01, Vol.381 (1), p.379-451
Main Authors: Christandl, Matthias, Leditzky, Felix, Majenz, Christian, Smith, Graeme, Speelman, Florian, Walter, Michael
Format: Article
Language:English
Subjects:
Asymptotic properties
Classical and Quantum Gravitation
Complex Systems
Dirichlet problem
Eigenvalues
Mathematical and Computational Physics
Mathematical Physics
Matrix theory
Optimization
Physics
Physics and Astronomy
Ports
Quantum computing
Quantum cryptography
Quantum Physics
Quantum teleportation
Relativity Theory
Theoretical
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Summary:Quantum teleportation is one of the fundamental building blocks of quantum Shannon theory. While ordinary teleportation is simple and efficient, port-based teleportation (PBT) enables applications such as universal programmable quantum processors, instantaneous non-local quantum computation and attacks on position-based 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 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 the way, we refine a convergence result for the fluctuations of the Schur–Weyl distribution by Johansson, which might be of independent interest.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03884-0