Optimal Multi-port-based Teleportation Schemes

TL;DR

This paper develops optimal multi-port quantum teleportation schemes, providing analytical solutions for success probability and fidelity, and demonstrating significant improvements over non-optimal methods using advanced mathematical tools.

Contribution

It introduces fully characterized optimal probabilistic and deterministic multi-port teleportation schemes with analytical solutions leveraging SDP and representation theory.

Findings

Square improvement in success probability with more ports

High efficiency for growing number of teleported systems

Analytical expressions for optimal measurements and shared states

Abstract

In this paper, we introduce optimal versions of a multi-port based teleportation scheme allowing to send a large amount of quantum information. We fully characterise probabilistic and deterministic case by presenting expressions for the average probability of success and entanglement fidelity. In the probabilistic case, the final expression depends only on global parameters describing the problem, such as the number of ports $N$, the number of teleported systems $k$, and local dimension $d$. It allows us to show square improvement in the number of ports with respect to the non-optimal case. We also show that the number of teleported systems can grow when the number $N$ of ports increases as $o(N)$ still giving high efficiency. In the deterministic case, we connect entanglement fidelity with the maximal eigenvalue of a generalised teleportation matrix. In both cases the optimal set of measurements and the optimal state shared between sender and receiver is presented. All the results are obtained by formulating and solving primal and dual SDP problems, which due to existing symmetries can be solved analytically. We use extensively tools from representation theory and formulate new results that could be of the separate interest for the potential readers.