Port-based teleportation in arbitrary dimension

TL;DR

This paper fully characterizes port-based teleportation protocols for any dimension and number of ports, introducing new mathematical tools and representation theory to analyze their performance efficiently.

Contribution

It develops the representation theory of partially transposed permutation operators, enabling polynomial-time analysis of PBT protocols for arbitrary dimensions.

Findings

Complete characterization of PBT performance for arbitrary dimensions

Introduction of the algebra of partially transposed permutation operators

Polynomial-time analysis of PBT schemes

Abstract

Port-based teleportation (PBT), introduced in 2008, is a type of quantum teleportation protocol which transmits the state to the receiver without requiring any corrections on the receiver's side. Evaluating the performance of PBT was computationally intractable and previous attempts succeeded only with small systems. We study PBT protocols and fully characterize their performance for arbitrary dimensions and number of ports. We develop new mathematical tools to study the symmetries of the measurement operators that arise in these protocols and belong to the algebra of partially transposed permutation operators. First, we develop the representation theory of the mentioned algebra which provides an elegant way of understanding the properties of subsystems of a large system with general symmetries. In particular, we introduce the theory of the partially reduced irreducible representations which we use to obtain a simpler representation of the algebra of partially transposed permutation operators and thus explicitly determine the properties of any PBT scheme for fixed dimension in polynomial time.