Higher-dimensional performance of port-based teleportation.

Zhi-Wei Wang,Samuel L. Braunstein

doi:10.1038/srep33004

Abstract

Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. However, its behavior for higher-dimensional systems has been hard to calculate explicitly beyond dimension d = 2. Indeed, relying on conventional Hilbert-space representations entails an exponential overhead with increasing dimension. Some general upper and lower bounds for various success measures, such as (entanglement) fidelity, are known, but some become trivial in higher dimensions. Here we construct a graph-theoretic algebra (a subset of Temperley-Lieb algebra) which allows us to explicitly compute the higher-dimensional performance of PBT for so-called “pretty-good measurements” with negligible representational overhead. This graphical algebra allows us to explicitly compute the success probability to distinguish the different outcomes and fidelity for arbitrary dimension d and low number of ports N, obtaining in addition a simple upper bound. The results for low N and arbitrary d show that the entanglement fidelity asymptotically approaches N/d2 for large d, confirming the performance of one lower bound from the literature.

Highlights

Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction
Port-based teleportation (PBT)[1] is a variation of conventional quantum teleportation, which can be used as a universal processor
Unlike conventional teleportation[2], PBT does not require any corrective unitary operation at Bob’s side other than to discard the unused ports, it achieves this at the cost of requiring more entanglement, while simultaneously realising only a finite probability of success

Summary

Introduction

Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. We construct a graph-theoretic algebra (a subset of Temperley-Lieb algebra) which allows us to explicitly compute the higher-dimensional performance of PBT for so-called “pretty-good measurements” with negligible representational overhead. This graphical algebra allows us to explicitly compute the success probability to distinguish the different outcomes and fidelity for arbitrary dimension d and low number of ports N, obtaining in addition a simple upper bound. There are several papers giving bounds to the performance of PBT more generally[3,5,6,7], but they do not explicitly calculate the achievable fidelity (or other performance measures) for higher dimensional systems. FiDn)alolyf,tihfiσs DC is teleportation is given by the so-called entanglement fidelity[8] for this process

Methods

Results

Conclusion