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arXiv:2411.09350 · Physical Review A

Nonlinear protocol for high-dimensional quantum teleportation

Luca Bianchi, Carlo Marconi, Giulia Guarda, Davide Bacco

Published Jun 25, 2025• 4 citations
arXivHTMLPDF

Abstract

Bell measurements, which allow entanglement between uncorrelated distant particles, play a central role in quantum communication. Indeed sharing, measuring and creating entanglement lie at the core of various protocols, such as entanglement swapping and quantum teleportation. While for optical qubit systems a Bell measurement can be implemented using only linear components, the same result is no longer true for high-dimensional states, where one has to consider either ancillary photons or nonlinear processes. Here, inspired by the latter approach, we propose a protocol for high-dimensional quantum teleportation based on nonlinear techniques. Moreover, we discuss the practical implementation of our proposed setup in the case of path-encoded qutrits, where nonlinear effects arise from sum-frequency generation. Finally, we compute the fidelity between quantum states to benchmark the validity of our model under the presence of crosstalk noise. Our approach is deterministic, scalable and does not rely on the use of auxiliary photons, thus paving the way towards the practical implementation of quantum networks based on nonlinear effects.

DOI
10.1103/3x44-664w

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Bell measurements, which allow entanglement between uncorrelated distant particles, play a central role in quantum communication. Indeed sharing, measuring and creating entanglement lie at the core of various protocols, such as entanglement swapping and quantum teleportation. While for optical qubit systems a Bell measurement can be implemented using only linear components, the same result is no longer true for high-dimensional states, where one has to consider either ancillary photons or nonlinear processes. Here, inspired by the latter approach, we propose a protocol for high-dimensional quantum teleportation based on nonlinear techniques. Moreover, we discuss the practical implementation of our proposed setup in the case of path-encoded qutrits, where nonlinear effects arise from sum-frequency generation. Finally, we compute the fidelity between quantum states to benchmark the validity of our model under the presence of crosstalk noise. Our approach is deterministic, scalable and does not rely on the use of auxiliary photons, thus paving the way towards the practical implementation of quantum networks based on nonlinear effects.
Quantum networking protocols, including quantum teleportation and entanglement swapping, use linear-optical Bell state measurements for heralding the distribution and transfer of quantum information. However, a linear-optical Bell state measurement requires identical photons and is susceptible to errors caused by multiphoton emission, fundamentally limiting the efficiency and fidelity of quantum networking protocols. Here we show a nonlinear Bell state analyzer for time-bin encoded photons based on a nanophotonic cavity with a sum-frequency generation efficiency of 4×10^{-5} to filter multiphoton emissions, and utilize it for faithful quantum teleportation involving spectrally distinct photons with fidelities ≥94% down to the single-photon level. Our result demonstrates that nonlinear-optical entangling operations, empowered by our efficient nanophotonics platform, can realize faithful quantum information protocols without requiring identical photons and without the fundamental limit on the fidelity of a Bell state measurement imposed by linear optics, which facilitates the realization of practical quantum networks.
Quantum teleportation have a central role in quantum information science and allows transferring of an unknown quantum state through entanglement and classical communication. Unfortunately, the interaction with external and internal noise severely affects the quality of teleportation and poses limitations on practical applications of quantum communication networks. In this work, instead of conventional Bell teleportation, we introduce a Machine Learned adaptive protocol for optimizing multiple components of Quantum Teleportation in order to achieve higher fidelity in various noise environments. In order to demonstrate the performance of the proposed scheme, we study three different noise models, including bit-flip, amplitude damping, and depolarizing noise, both in case of single-qubit and two-qubit channels. As a result, we observe substantial improvement in the teleportation fidelity in comparison to the classical Bell-state teleportation protocol in certain noise conditions. Furthermore, the machine-learned protocol reveals a nontrivial strategy for compensation of decoherence and information losses. In addition, obtained results indicate the flexibility and reliability of the proposed framework for implementing various adaptive quantum communications while shedding light on possibilities of discovery of optimal quantum algorithms by means of automated approache
Quantum teleportation provides a way to transmit unknown quantum states from one location to another. In the quantum world, multilevel systems which enable high-dimensional systems are more prevalent. Therefore, to completely rebuild the quantum states of a single particle remotely, one needs to teleport multilevel (high-dimensional) states. Here, we demonstrate the teleportation of high-dimensional states in a three-dimensional six-photon system. We exploit the spatial mode of a single photon as the high-dimensional system, use two auxiliary entangled photons to realize a deterministic three-dimensional Bell state measurement. The fidelity of teleportation process matrix is F=0.596±0.037. Through this process matrix, we can prove that our teleportation is both nonclassical and genuine three dimensional. Our work paves the way to rebuild complex quantum systems remotely and to construct complex quantum networks.
Entanglement in high-dimensional systems plays a vital role in quantum information processing (QIP), as it extends the available Hilbert space, supports the manipulation of more intricate information, and broadens the scope of implementable quantum operations. In the paper, we present a deterministic scheme for the four-dimensional two-qudit Bell entangled state analysis for the four-photon system in the polarization degree of freedom, resorting to the weak cross-Kerr nonlinearity and some linear optical components. In our scheme, the analysis of four-dimensional Bell entangled state is constructed by three-photon Toffoli gate and quantum nondemolition detectors (QND 1 and QND 2 ). By phase shifts of the coherent beams, the 16 orthogonal four-dimensional two-qudit Bell states can be completely distinguished from each other. The proposal can be extended to the four-dimensional three-qudit entangled state analysis and n -qudit entangled state analysis. In addition, our deterministic scheme for high-dimensional entangled state analysis can be applied to high-dimensional quantum teleportation, including both uncontrolled and controlled quantum teleportation protocols. Moreover, our scheme can achieve high fidelity and efficiency, further broadening its applicability in high-dimensional QIP.
Quantum teleportation allows a "disembodied" transmission of unknown quantum states between distant quantum systems. Yet, all teleportation experiments to date were limited to a two-dimensional subspace of quantized multiple levels of the quantum systems. Here, we propose a scheme for teleportation of arbitrarily high-dimensional photonic quantum states and demonstrate an example of teleporting a qutrit. Measurements over a complete set of 12 qutrit states in mutually unbiased bases yield a teleportation fidelity of 0.75(1), which is well above both the optimal single-copy qutrit state-estimation limit of 1/2 and maximal qubit-qutrit overlap of 2/3, thus confirming a genuine and nonclassical three-dimensional teleportation. Our work will enable advanced quantum technologies in high dimensions, since teleportation plays a central role in quantum repeaters and quantum networks.
Bell state measurements (BSMs) of photonic qubits are used for quantum networking protocols to herald the distribution and transfer of quantum information. However, standard BSMs based on linear optics (LO-BSMs) require identical photons and are susceptible to errors from multiphoton emissions, leading to reduced fidelity of protocols, particularly in the absence of postselection. To overcome these challenges, Bell state measurements based on nonlinear optics (NLO-BSMs) have been proposed and implemented, leveraging sum-frequency generation (SFG) to filter out multiphoton emissions and improve the fidelity without postselection. Here we analyze the fidelity of LO-BSM and NLO-BSM heralded entanglement swapping in lossy channels and compare their performance under realistic conditions. We also explore the impact of state-of-the-art nonlinear photonics platforms on SFG efficiency and highlight how advances in nanophotonics will enable practical, high-fidelity NLO-BSM-based quantum networking applications.