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arXiv:2312.01519 · Physical Review Research

Error correlations in photonic qudit-mediated entanglement generation

Xiaoyu Liu, Niv Bharos, Liubov A. Markovich, Johannes Borregaard

Published Apr 22, 2024• 1 citation
arXivHTMLPDF

Abstract

Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pairs, which can significantly reduce the required coherence time of the qubit registers. However, current schemes require fast optical switching, which is experimentally challenging. In addition, the higher degree of error correlation between the generated entangled pairs in qudit protocols compared to qubit protocols has not been widely studied in detail. We propose a qudit-mediated entangling protocol that completely circumvents the need for optical switches at the expense of a lower success probability of the scheme. Furthermore, we quantify the amount of error correlation between the simultaneously generated entangled pairs and analyze the effect on entanglement purification algorithms and teleportation-based quantum error correction. We find that optimized purification schemes can efficiently correct the correlated errors, while the quantum error correction codes studied here perform worse than for uncorrelated error models. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023075

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Generating entanglement between distributed network nodes is a prerequisite for the quantum internet. Entanglement distribution protocols based on high-dimensional photonic qudits enable the simultaneous generation of multiple entangled pairs, which can significantly reduce the required coherence time of the qubit registers. However, current schemes require fast optical switching, which is experimentally challenging. In addition, the higher degree of error correlation between the generated entangled pairs in qudit protocols compared to qubit protocols has not been widely studied in detail. We propose a qudit-mediated entangling protocol that completely circumvents the need for optical switches at the expense of a lower success probability of the scheme. Furthermore, we quantify the amount of error correlation between the simultaneously generated entangled pairs and analyze the effect on entanglement purification algorithms and teleportation-based quantum error correction. We find that optimized purification schemes can efficiently correct the correlated errors, while the quantum error correction codes studied here perform worse than for uncorrelated error models. Published by the American Physical Society 2024
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Entanglement generation between distant nodes is a fundamental process in distributed quantum information processing. Qudits, high-dimensional quantum states, are promising candidates for enhancing entanglement distribution capabilities. However, the success probability of qudit entanglement distribution using Bell measurements is typically lower than that of conventional qubit-based protocols. In this paper, we propose an entanglement swapping protocol specifically designed for qutrits (three-dimensional quantum states). Our protocol employs photon-number encoding combined with an additional mode basis, such as polarization, effectively increasing the success probability. We show that the proposed qutrit protocol can achieve higher entanglement generation rates compared to conventional two-photon detection-based qubit protocols, especially under conditions of limited photon generation probability. Furthermore, we evaluate our protocol under realistic experimental imperfections, including photon loss and threshold detection, and show that it achieves high fidelity with probabilistic photon sources.
The generation of entanglement between distant quantum systems is at the core of quantum networking. In recent years, numerous theoretical protocols for remote-entanglement generation have been proposed, many of which have been experimentally realized. Here, we provide a modular theoretical framework to elucidate the general mechanisms of photon-mediated entanglement generation between single spins in atomic or solid-state systems. Our framework categorizes existing protocols at various levels of abstraction and allows for combining the elements of different schemes in new ways. These abstraction layers make it possible to readily compare protocols for different quantum hardware. To enable the practical evaluation of protocols tailored to specific experimental parameters, we have devised numerical simulations based on the framework with our codes available online. Published by the American Physical Society 2024
The use of higher-dimensional photonic encodings (qudits) instead of two-dimensional encodings (qubits) can improve the loss tolerance and reduce the computational resources of photonic-based quantum information processing. To harness this potential, efficient schemes for entangling operations such as the high-dimensional generalization of a linear optics Bell measurement will be required. We show how an efficient high-dimensional entangled state analyzer can be implemented with a linear optics interferometer and auxiliary photonic states. The degree of entanglement of the auxiliary state is much less than in previous protocols as quantified by an exponentially smaller Schmidt rank. In addition, the auxiliary state only occupies a single spatial mode, allowing it to be generated deterministically from a single quantum emitter coupled to a small qubit register. The reduced complexity of the auxiliary states results in a high robustness to imperfections and we show that auxiliary states with fidelities above 0.9 for qudit dimensions 4 can be generated in the presence of qubit error rates on the order of 10%. This paves the way for experimental demonstrations with current hardware.
Multiple photonic degrees of freedom can be explored to generate high-dimensional quantum states; commonly referred to as `qudits'. Qudits offer several advantages for quantum communications, including higher information capacity, noise resilience and data throughput, and lower information loss over different propagation mediums (free space, optical fibre, underwater) as compared to conventional qubits based communication system. However, qudits have been little exploited in literature, owing to their difficulty in transmission and detection. In this paper, for the first time, we develop and formulate the theoretical framework for transmission of classical information through entanglement distribution of qudits over two quantum channels in superposition of alternative causal order. For the first time we i) engineer quantum switch operation for 2-qudit systems and ii) formulate theoretical system model for entanglement distribution of qudits via quantum switch. Results show that entanglement distribution of a qudit provides a considerable gain in fidelity even with increase in noise.
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