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arXiv:2105.03586

Overcoming the repeaterless bound in continuous-variable quantum communication without quantum memories

Matthew S. Winnel, Joshua J. Guanzon, Nedasadat Hosseinidehaj, Timothy C. Ralph

Published May 8, 2021• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2105.03586

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•Jan 17, 2020•1 citation
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.
Quantum repeaters have been proposed as a way of extending the reach of quantum communication. First-generation approaches use entanglement swapping to connect entangled links along a long-distance channel. Recently, there have been proposals for first-generation quantum repeaters for continuous variables. In this paper, we present an improved continuous-variable (CV) repeater scheme using optimal Gaussian entanglement swapping. Our scheme uses the noiseless linear amplifier for entanglement distillation. We show that with the simplest configuration of the noiseless linear amplifier and under the assumption of good quantum memories and perfect sources and detectors, our scheme beats the direct transmission upper limit for shorter distances and can offer advantages over previous CV repeater schemes.
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.
The field of quantum communications promises the faithful distribution of quantum information, quantum entanglement, and absolutely secret keys. However, the highest rates of these tasks are fundamentally limited by the transmission distances. Quantum repeaters are necessary to overcome the repeaterless bound which sets the fundamental rate-distance limit of any repeaterless quantum communication protocol. The ultimate end-to-end rates of quantum repeater networks are known to be achievable by an optimal entanglement-distillation protocol followed by quantum teleportation. In this thesis, we give physical repeater designs for this achievability. We also propose practical repeater designs with near-term potential for real-world practical applications.
We investigate the use of quantum scissors, as candidates for non-deterministic amplifiers, in continuous-variable quantum key distribution. Such devices rely on single-photon sources for their operation and as such, they do not necessarily preserve the Guassianity of the channel. Using exact analytical modeling for the system components, we bound the secret key generation rate for a protocol that uses quantum scissors. We find that, for certain non-zero values of excess noise, such a protocol can reach longer distances than the counterpart with no amplification. This sheds light into the prospect of using quantum scissors as an ingredient in continuous-variable quantum repeaters.
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 communication enables various technological possibilities that are hard or impossible with classical communication. These include secure distribution of keys, transfer of quantum information and distributed quantum computation and sensing. Quantum communication relies on the ability to transmit a quantum state over some distance. Exponential photon loss from fibre inevitably limits the distance one would be able to achieve this over and therefore make use of these promising new technologies.Quantum repeaters have been proposed as a solution to this problem. Elementary repeater protocols involve dividing the channel into smaller segments with repeater nodes, distributing entanglement between these nodes and then performing swapping operations to connect entangled pairs and purification to correct operation errors. In the years since these elementary protocols, quantum repeaters have been through extensive theoretical improvements including utilising the benefits of quantum error correction to improve efficiency.However, the vast majority of these protocols are for discrete encodings of quantum information. There is significant interest in using continuous variable encodings of quantum information for quantum communication applications. This is motivated in part by the ease of generating, manipulating and detecting quantum states and additionally the increased compatibility with existing infrastructure. In this thesis we present one of the first quantum repeater protocols for continuous variable encodings of quantum information.The continuous variable quantum repeater we present in this thesis is based on concatenated error correction protocols that work to correct loss on any optical field state. We thoroughly investigate operation of this error correction protocol including the trade-offs associated with real implementations, various modifications to the error correction protocol as well as whether it can be implemented with current technology.We illustrate how these error correction protocols may be structured to form a quantum repeater that inhibits the exponential photon loss problem with a resource cost that scales polynomially with distance. We show that our continuous variable repeater is able to beat the fundamental bound on quantum communication without a repeater. Finally, we compare the performance of our first generation continuous variable repeater to existing first generation discrete variable protocols.