Quantum teleportation in high dimensions

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.

• The paper introduces a novel protocol for teleporting qutrit states with an experimental fidelity of 0.75, clearly exceeding classical thresholds.
• The experiment utilizes high-dimensional Bell-state measurements through a hybrid polarization-path setup and multi-port interferometer to ensure precise phase stability.
• These results pave the way for robust quantum networks and integrated photonics, enhancing applications like device-independent quantum key distribution.

Quantum Teleportation in High Dimensions: An Exploration of Qutrits

The study of quantum teleportation has long been confined to two-dimensional systems, commonly known as qubits. This paper proposes and experimentally demonstrates a novel scheme for teleporting high-dimensional quantum states—specifically qutrits, or three-level systems. The authors report a teleportation fidelity of 0.75, significantly surpassing the classical limit of 0.5. This fidelity also exceeds the maximal overlap of qutrit states with qubit states, which has a threshold of 2/3, thus verifying a genuine three-dimensional teleportation.

Methodology and Experimentation

The authors outline a protocol for high-dimensional quantum teleportation, using a three-level photonic system as an exemplary case. The teleportation process is facilitated by pre-shared high-dimensional entangled states between two parties, Alice and Bob. A critical component of this scheme is the high-dimensional Bell-state measurement (BSM), which projects the entangled state and the state to be teleported onto one of the possible high-dimensional Bell states. As detailed, the success probability of this technique is 1/81, which can be enhanced to 1/9 with active feed-forward mechanisms.

The experimental setup employs a femtosecond pulsed laser to generate entangled photon pairs. These photons are then processed through a network of beam splitters and wave plates to perform the high-dimensional BSM. Due to the intricate nature of high-dimensional teleportation, maintaining phase stability and precision is paramount. The authors utilize a hybrid polarization-path encoding and a multi-port interferometer to achieve this.

Results and Verification

The authors assess the fidelity of their teleportation prototype over a minimal set of 12 states derived from mutually unbiased bases. The experimental configuration allows the determination of three-level quantum state fidelities, achieving an average of 0.75 across measured cases. This superior performance over classical methods corroborates the non-classicality of the teleportation protocol. Furthermore, the experimental data affirm that the teleportation preserves the coherence of superpositions across all three dimensions, refuting any hypothesis of lower-dimensional state representations.

Implications and Future Directions

Establishing operational protocols for high-dimensional quantum teleportation paves the way for advanced quantum communication technologies, offering both increased capacity and robustness against noise compared to traditional qubit systems. This demonstration invites further exploration into the teleportation of quantum states with more than three dimensions, potentially incorporating orbital angular momentum or other degrees of freedom.

In practical terms, these advancements could be seamlessly adapted to integrated photonics platforms. Moreover, the framework presented opens avenues for investigating the teleportation of complex quantum systems, including multi-particle and composite-state teleportation. The fully realized potential of these high-dimensional systems expands possibilities for robust quantum networks, particularly in the context of entanglement swapping and device-independent quantum key distribution.

Conclusion

This study marks a pivotal evolution in the domain of quantum teleportation by extending the established principles to high-dimensional quantum systems like qutrits. With its profound implications for quantum communication and foundational studies of quantum mechanics, further investigation of high-dimensional quantum teleportation might reveal new phenomena and practical applications that transcend current technological boundaries.