# Quantum teleportation in high dimensions

## TL;DR

This paper demonstrates the first experimental teleportation of a high-dimensional quantum state (a qutrit), surpassing qubit limitations and enabling advanced quantum communication and information processing.

## Contribution

It introduces a resource-efficient, extendable scheme for teleporting arbitrary high-dimensional photonic quantum states and reports the first experimental realization of a qutrit teleportation.

## Key findings

- Achieved a teleportation fidelity of 0.75 for a qutrit, exceeding classical limits.
- Proved genuine three-dimensional, universal quantum teleportation.
- Provided a comprehensive toolbox for teleporting quantum particles with multiple degrees of freedom.

## Abstract

Precise measurement or perfect cloning of unknown quantum states is forbidden by the laws of quantum mechanics. Yet, quantum teleportation in principle allows for a faithful and disembodied transmission of unknown quantum states between distant quantum systems using entanglement. There have been numerous experiments on teleportation of quantum states of single photons, atoms, trapped ions, defects in solid states, and superconducting circuits. However, all demonstrations to date were limited to a two-dimensional subspace$-$so-called qubit$-$of the quantized multiple levels of the quantum systems. In general, a quantum particle can naturally possess not only multiple degrees of freedom, but also, many degrees of freedom can have high quantum number beyond the simplified two-level subspace. Here, making use of multiport beam-splitters and ancillary single photons, we propose a resource-efficient and extendable scheme for teleportation of arbitrarily high-dimensional photonic quantum states. We report the first experimental teleportation of a qutrit, which is equivalent to a spin-1 system. Measurements over a complete set of 12 states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), well above the optimal single-copy qutrit-state-estimation limit of 1/2. The fidelity also exceeds the limit of 2/3, the maximum possible for explanation through qubits only. Thus, we strictly prove a genuine three-dimensional, universal, and highly non-classical quantum teleportation. Combining previous methods of teleportation of two-particle composite states and multiple degrees of freedom, our work provides a complete toolbox for teleporting a quantum particle intact. We expect that our results will pave the way for quantum technology applications in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.

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Source: https://tomesphere.com/paper/1906.09697