Asymptotic performance of port-based teleportation

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Port-based teleportation (PBT) is a variant of the well-known task of quantum teleportation in which Alice and Bob share multiple entangled states called "ports". While in the standard teleportation protocol using a single entangled state the receiver Bob has to apply a non-trivial correction unitary, in PBT he merely has to pick up the right quantum system at a port specified by the classical message he received from Alice. PBT has applications in instantaneous non-local computation and can be used to attack position-based quantum cryptography. Since perfect PBT protocols are impossible, 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, without loss of generality the resource state can be assumed to have a “purified" Schur-Weyl duality symmetry. I will give an introduction to the task of PBT and its symmetries, and show how the asymptotics of existing formulas for the optimal performance for a given number of ports can be derived using a connection between representation theory and the Gaussian unitary ensemble.

Joint work with M. Christandl, C. Majenz, G. Smith, F. Speelman & M. Walter