Optimal Port-based Teleportation

TL;DR

This paper characterizes the optimal performance of deterministic port-based teleportation, revealing that the maximum fidelity is determined by the largest eigenvalue of a specific matrix called the Teleportation Matrix.

Contribution

It introduces the Teleportation Matrix and provides a complete characterization of the optimal fidelity for dPBT with arbitrary ports and dimensions.

Findings

Optimal fidelity is given by the largest eigenvalue of the Teleportation Matrix.

The Teleportation Matrix encodes relationships between Young diagrams.

The results are derived through semidefinite programming analysis.

Abstract

Deterministic port-based teleportation (dPBT) protocol is a scheme where a quantum state is guaranteed to be transferred to another system without unitary correction. We characterize the best achievable performance of the dPBT when both the resource state and the measurement is optimized. Surprisingly, the best possible fidelity for an arbitrary number of ports and dimension of the teleported state is given by the largest eigenvalue of a particular matrix -- Teleportation Matrix. It encodes the relationship between a certain set of Young diagrams and emerges as the the optimal solution to the relevant semidefinite program.