Generalizing teleportation

Generalized teleportation and entanglement recycling
Sergii Strelchuk,1, ∗ Michał Horodecki,2 and Jonathan Oppenheim3 of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, U.K. 2 Institute for Theoretical Physics and Astrophysics, University of Gdansk, 80-952 Gdansk, Poland ´ ´ 3 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, U.K. University College of London, Department of Physics & Astronomy, London, WC1E 6BT and London Interdisciplinary Network for Quantum Science
1 Department

arXiv:1209.2683v2 [quant-ph] 13 Dec 2012

We introduce new teleportation protocols which are generalizations of the original teleportation protocols that use the Pauli group [1] and the port-based teleportation protocols, introduced by Hiroshima and Ishizaka [2], that use the symmetric permutation group. We derive sufficient condition for a set of operations, which in general need not form a group, to give rise to a teleportation protocol and provide examples of such schemes. This generalization leads to protocols with novel properties and is needed to push forward new schemes of computation based on them. Port-based teleportation protocols and our generalizations use a large resource state consisting of N singlets to teleport only a single qubit state reliably. We provide two distinct protocols which recycle the resource state to teleport multiple states with error linearly increasing with their number. The first protocol consists of sequentially teleporting qubit states, and the second teleports them in a bulk.

Teleportation lies at the very heart of quantum information theory, being the pivotal primitive in a variety of tasks. Teleportation protocols are a way of sending an unknown quantum state from one party to another using a resource in the form of an entangled state shared between two parties, Alice and Bob, in advance. First, Alice performs a measurement on the state she wants to