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arXiv:2411.14757 · Quantum Science and Technology

Continuous-variable multiplexed quantum repeater networks

Pei‐Zhe Li, William J. Munro, Kae Nemoto, Nicoló Lo Piparo

Published Mar 25, 2025• 2 citations
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Abstract

Abstract Continuous-variable (CV) codes and their application in quantum communication have attracted increasing attention. In particular, one typical CV codes, cat-codes, has already been experimentally created using trapped atoms in cavities with relatively high fidelities. However, when these codes are used in a repeater protocol, the secret key rate (SKR) that can be extracted between two remote users is extremely low. Here we propose a quantum repeater protocol based on cat codes with a few quantum memories or graph states as additional resources. This allows us to considerably increase the SKR by several orders of magnitude. Our findings provide valuable insights for designing efficient quantum repeater systems, advancing the feasibility and performance of quantum communication over long distances.

DOI
10.1088/2058-9565/adc500

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Abstract Continuous-variable (CV) codes and their application in quantum communication have attracted increasing attention. In particular, one typical CV codes, cat-codes, has already been experimentally created using trapped atoms in cavities with relatively high fidelities. However, when these codes are used in a repeater protocol, the secret key rate (SKR) that can be extracted between two remote users is extremely low. Here we propose a quantum repeater protocol based on cat codes with a few quantum memories or graph states as additional resources. This allows us to considerably increase the SKR by several orders of magnitude. Our findings provide valuable insights for designing efficient quantum repeater systems, advancing the feasibility and performance of quantum communication over long distances.
In present-day quantum communications, one of the main problems is the lack of a quantum repeater design that can simultaneously secure high rates and long distances. Recent literature has established the end-to-end capacities that are achievable by the most general protocols for quantum and private communication within a quantum network, encompassing the case of a quantum repeater chain. However, whether or not a physical design exists to approach such end-to-end capacities remains a challenging objective. Driven by this motivation, in this work we put forward a design for continuous-variable quantum repeaters and show that it can actually achieve the feat. We also show that even in a noisy regime, our rates surpass the Pirandola-Laurenza-Ottaviani-Banchi bound. Our repeater setup is developed upon using noiseless linear amplifiers, quantum memories, and continuous-variable Bell measurements. Furthermore, we propose a nonideal model for continuous-variable quantum memories that we make use of in our design. We then show that potential quantum communication rates would deviate from the theoretical capacities, as one would expect, if the quantum link is too noisy, and/or if low-quality quantum memories and amplifiers are employed.
Quantum repeaters represent one possible way to achieve long-distance quantum key distribution. Collins et al. [O. A. Collins, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, Phys. Rev. Lett. 98, 060502 (2007)] proposed multiplexing as a method to increase the repeater rate and to decrease the requirement of memory coherence time. Motivated by the experimental fact that long-range connections are practically demanding, in this paper we extend the original quantum repeater multiplexing protocol to the case of short-range connection. We derive analytical formulas for the repeater rate and we show that for short connection lengths it is possible to have most of the benefits of a full-range multiplexing protocol. Then we incorporate decoherence of quantum memories and we study the optimal matching for the Bell-state measurement protocol permitting us to minimize the memory requirements. Finally, we calculate the secret key rate and we show that the improvement via finite-range multiplexing is of the same order of magnitude as that via full-range multiplexing.
One of the main problems in quantum communications is how to achieve high rates at long distances. Quantum repeaters, i.e., untrusted, intermediate relay stations, are necessary to overcome the repeaterless bound which sets the fundamental rate-distance limit of repeaterless communications. In this work, we introduce a continuous-variable protocol which overcomes the repeaterless bound and scales like the single-repeater bound using just one linear-optical device called a "quantum scissor", combining the entanglement distillation and entanglement swapping elements of previous repeater proposals into a single step, thus, removing the need for quantum memories. Implementing a standard continuous-variable quantum key distribution protocol using our repeater we predict key rates which surpass the repeaterless bound. Our protocol works well for non-ideal single-photon sources and non-ideal single-photon detectors, and can tolerate some level of excess noise, making our protocol implementable with existing technology. We show that our scheme can be extended to longer repeater chains using quantum memories, using less physical resources than previous schemes. Furthermore, for applications beyond key distribution, our scheme generalises to higher order and distils more entanglement at the cost of a reduced probability of success.
Long-distance quantum communication necessitates the use of quantum repeaters, which typically include highly coherent quantum memories. We provide a theoretical analysis of the secret key rates for a quantum repeater system incorporating bosonic error correction and memory components. Specifically, we focus on the application of Binomial codes for two repeater segments. Using these codes, our investigation aims to suppress memory loss errors that commonly affect systems such as atoms and microwave cavities, in contrast to dephasing errors in single-spin memories. We further discuss a physical implementation of such a quantum repeater comprising a microwave cavity and a superconducting transmon, capable of state engineering with high fidelities (>97%>97\%>97%) and logical Bell state measurements for successful entanglement swapping. As an alternative approach, we also discuss a realization in the all-optical domain.
Optical telecommunication is at the heart of today's internet and is currently enabled by the transmission of intense optical signals between remote locations. As we look to the future of telecommunication, quantum mechanics promise new ways to be able to transmit and process that information. Demonstrations of quantum key distribution and quantum teleportation using multiphoton states have been performed, but only over ranges limited to a few hundred kilometers. To go beyond this, we need repeaters that are compatible with these quantum multiphoton continuous-variable pulses. Here we present a design for continuous-variable quantum repeaters that can distribute entangled and pure two-mode squeezed states over arbitrarily long distances with a success probability that scales only polynomially with distance. The proposed quantum repeater is composed from several basic known building blocks such as non-Gaussian operations for entanglement distillation and an iterative Gaussification protocol (for retaining the Gaussian character of the final state), but complemented with a heralded non-Gaussian entanglement swapping protocol, which allows us to avoid extensive iterations of quantum Gaussification. We characterize the performance of this scheme in terms of key rates for quantum key distribution and show a secure key can be generated over thousands of kilometers.
Abstract A quantum repeater scheme based on cavity‐quantum electrodynamics (QED) and quantum error correction of channel loss via rotation‐symmetric bosonic codes (RSBCs) is proposed to distribute atomic entangled states over long distances without memories and at high clock rates. In this scheme, controlled rotation gates, i.e., phase shifts of the propagating light modes conditioned upon the state of an atom placed in a cavity, provide a mechanism both for the entangled‐state preparations and for the error syndrome identifications. In order to assess the performance of this repeater protocol, an explicit instance of RSBCs—multicomponent cat codes—are studied quantitatively. It is found that the total fidelity and the success probability for quantum communication over a long distance (such as 1000 km) both can almost approach unity provided a small enough elementary distance between stations (smaller than 0.1 or 0.01 km) and rather low local losses (up to 0.1%) are considered. In a quantum key distribution application, secret key rates can become correspondingly high, both per channel use, beating the repeaterless bound, and per second thanks to the relatively high clock rates of the memoryless scheme. Based upon the cavity‐QED setting, this scheme can be realized at room temperature and at optical frequencies.