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Port-based teleportation (PBT) is a variant of the well-known task of quantum teleportation where the receiver Bob, instead of having to apply a non-trivial correction unitary, merely has to pick up the right quantum system at a “port” specified by the classical message he received from Alice. While much more resource-demanding than standard teleportation, PBT has applications to instantaneous non-local computation and can be used to attack position-based quantum cryptography. A perfect PBT protocol would violate the linearity of quantum theory, so there is a trade-off between error and entanglement consumption (or the number of ports) which can be analyzed using representation theory of the symmetric and unitary groups. In particular the resource state has a “purified" Schur-Weyl duality symmetry. I will give an introduction to the task of PBT and its symmetries. Subsequently, I will present how the asymptotics of existing formulas for the optimal performance for a given number of ports can be derived. To achieve this, a connection between representation theory and the random matrix ensemble GUE_0, and a surprising appearance of the discrete Laplacian are exploited.

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Christian Majenz, QuSoft Amsterdam
Seminar room 0.01, ETP
Contact: David Gross