Multiphoton emissions constitute a fundamental source of noise in quantum repeaters and other quantum communication protocols when probabilistic photon sources are employed. In this paper it is shown that by alternating the Bell state measurement basis in concatenated entanglement swapping links one can automatically identify and discard many errors from stimulated multiphoton emissions. The proposed protocol is shown to completely eliminate the dominant quadratic growth of multiphoton errors with the length of the repeater chain. Furthermore, it is shown that the protocol can be employed in satellite-assisted entanglement distribution links to enable links which are more robust in the presence of imbalanced channel losses. The analysis introduces a convenient calculus based on Clifford algebra for modeling concatenated entanglement swapping links with multiphoton emissions. In particular, we present a compact expression for the fidelity of the Bell state produced by a repeater chain of arbitrary length including noise from double-pair emissions.
Multiphoton emissions constitute a fundamental source of noise in quantum repeaters and other quantum communication protocols when probabilistic photon sources are employed. In this paper it is shown that by alternating the Bell state measurement basis in concatenated entanglement swapping links one can automatically identify and discard many errors from stimulated multiphoton emissions. The proposed protocol is shown to completely eliminate the dominant quadratic growth of multiphoton errors with the length of the repeater chain. Furthermore, it is shown that the protocol can be employed in satellite-assisted entanglement distribution links to enable links which are more robust in the presence of imbalanced channel losses. The analysis introduces a convenient calculus based on Clifford algebra for modeling concatenated entanglement swapping links with multiphoton emissions. In particular, we present a compact expression for the fidelity of the Bell state produced by a repeater chain of arbitrary length including noise from double-pair emissions.
We propose a method to directly recover the degree of entanglement distributed by entanglement swapping in the presence of noise. Our approach introduces a reversing operation that probabilistically undoes the effect of amplitude damping or photon loss on a single entangled pair, enabling heralded recovery of entanglement. We demonstrate that entanglement can be substantially recovered even under strong noise, including parameter regimes where the distributed entanglement would otherwise vanish due to entanglement sudden death. We analyze the effectiveness of the protocol in two representative repeater models, i.e.,~two-way and one-way architectures and identify the optimal reversing strategy. Due to its heralded and single-copy nature, our protocol is readily compatible with other entanglement recovery techniques such as entanglement purification and distillation. Our work provides a practical and experimentally feasible way toward robust entanglement distribution in current and near-term quantum repeater architectures.
Quantum communications enable secure key transmission and entanglement distribution, but their rates and maximum transmission distances are limited due to the losses and noise introduced by quantum channels. Various techniques have been developed to address these limitations, tailored to the platform and the nature of the decoherence. In this thesis, we explore ways to enhance the performance of quantum communications, with a particular focus on increasing the key rates and transmission distances in quantum key distribution (QKD), a method that leverages quantum mechanics to securely share keys between trusted parties. Additionally, we aim to improve the purity of entangled states shared between two parties, contributing to broader advancements in quantum communications. We begin by introducing a software-enhanced continuous-variable QKD (CV-QKD) protocol, where keys are encoded onto the phase and amplitude degrees of the optical field. This protocol enhances both transmission distance and key rates through a post-selection method employing arbitrary filters, experimentally demonstrated on two different platforms. Its adaptability makes it highly promising, as it can be implemented on existing CV-QKD platforms and dynamically optimises key rates for rapidly changing channels. We then present a protocol for the pure-loss channel leveraging quantum repeaters to mitigate the channel losses by segmenting the total communication distance into smaller, more manageable intervals. This repeater-like protocol introduces a more efficient entanglement-swapping measurement at the repeater station than the state-of-the-art twin-field protocols. Instead of polarisation encoding, our protocol relies on encoding keys in the photon-number basis, optimising the states to achieve the highest key rates for each distance. Notably, this protocol shows strong potential for improving long-distance quantum communication by surpassing the capacity of the direct communication channel at a shorter distance than the existing repeater protocols such as twin-field QKD while achieving an overall higher transmission distance. Finally, in this thesis, we demonstrate that for the Pauli-dephasing channel, placing a node in the middle of the quantum channel to perform a Bell-state measurement as an entanglement-swapping operation does not result in improved key rates, even with reduced decoherence. As a result, we propose an entanglement purification protocol that refines a larger set of noisy entangled states into a smaller set of high-fidelity ones using local operations and classical communication. This purification protocol builds upon earlier purification methods, extending their application from two Bell pairs to any number of Bell pairs and thereby achieving the capacity of the dephasing channel. Through numerous recursive iterations, it produces near-perfect Bell pairs, making it well-suited for quantum repeaters and correcting dephasing errors in quantum computers.
Measurement-based quantum repeaters employ entanglement distillation and swapping across links using locally prepared resource states of minimal size and local Bell measurements. In this Letter, we introduce a systematic protocol for measurement-based entanglement distillation and its application to repeaters that can leverage any stabilizer code. Given a code, we explicitly define the corresponding resource state and derive an error-recovery operation based on all Bell measurement outcomes. Our approach offers deeper insights into the impact of resource state noise on repeater performance while also providing strategies for efficient preparation and fault-tolerant preservation of resource states. As an application, we propose a measurement-based repeater protocol based on quantum low-density parity-check (QLDPC) codes, enabling constant-yield Bell state distribution over arbitrary distances. Numerical simulations identify a fault-tolerant threshold on the total physical error per repeater segment-including errors on resource states, remotely generated Bell states, and Bell measurements-and confirm that increasing the QLDPC code size further suppresses the logical error while maintaining a fixed encoding rate. This Letter establishes a scalable backbone for future global-scale fault-tolerant quantum networks.
We analyze an entanglement-based quantum key distribution (QKD) architecture that uses a linear chain of quantum repeaters employing photon-pair sources, spectral-multiplexing, linear-optic Bell-state measurements, multimode quantum memories, and classical-only error correction. Assuming perfect sources, we find an exact expression for the secret-key rate, and an analytical description of how errors propagate through the repeater chain, as a function of various loss-and-noise parameters of the devices. We show via an explicit analytical calculation, which separately addresses the effects of the principle nonidealities, that this scheme achieves a secret-key rate that surpasses the Takeoka-Guha-Wilde bound---a recently found fundamental limit to the rate-vs-loss scaling achievable by any QKD protocol over a direct optical link---thereby providing one of the first rigorous proofs of the efficacy of a repeater protocol. We explicitly calculate the end-to-end shared noisy quantum state generated by the repeater chain, which could be useful for analyzing the performance of other non-QKD quantum protocols that require establishing long-distance entanglement. We evaluate that shared state's fidelity and the achievable entanglement-distillation rate, as a function of the number of repeater nodes, total range, and various loss-and-noise parameters of the system. We extend our theoretical analysis to encompass sources with nonzero two-pair-emission probability, using an efficient exact numerical evaluation of the quantum state propagation and measurements. We expect our results to spur formal rate-loss analysis of other repeater protocols and also to provide useful abstractions to seed analyses of quantum networks of complex topologies.
Abstract Long-distance entanglement is a very precious resource, but its distribution is very difficult due to the exponential losses of light in optical fibres. A possible solution consists in the use of quantum repeaters, based on entanglement swapping (ES) or quantum error correction. Alternatively, satellite-based free-space optical links can be exploited, achieving better loss-distance scaling. We propose to combine these two ingredients, quantum repeaters and satellite-based links, into a scheme that allows to achieve entanglement distribution over global distances with a small number of intermediate untrusted nodes. The entanglement sources, placed on satellites, send quantum states encoded in photons towards orbiting quantum repeater stations, where ES is performed. The performance of this repeater chain is assessed in terms of the secret key rate achievable by the BBM92 cryptographic protocol. We perform a comparison with other repeater chain architectures and show that our scheme, even though more technically demanding, is superior in many situations of interest. Finally, we analyse strengths and weaknesses of the proposed scheme and discuss exemplary orbital configurations. The integration of satellite-based links with ground repeater networks can be envisaged to represent the backbone of the future quantum internet.