Generalized teleportation and entanglement recycling

TL;DR

This paper introduces generalized teleportation protocols that extend existing methods, enabling resource recycling for multiple qubit teleports with linearly increasing error, thus advancing quantum computation schemes.

Contribution

It develops a broad framework for teleportation protocols beyond groups, including resource recycling techniques for multiple qubits, enhancing efficiency and scalability.

Findings

Protocols recycle resource states for multiple qubits

Error increases linearly with number of teleported states

New general conditions for teleportation schemes

Abstract

We introduce new teleportation protocols which are generalizations of the original teleportation protocols that use the Pauli group [Bennett, et al. Physical Review Letters, 70(13) 1895-1899] and the port-based teleportation protocols, introduced by Hiroshima and Ishizaka [Physical Review Letters, 101(24) 240501], 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.