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arXiv:1611.02795 · Physical Review A

Repeaters for continuous-variable quantum communication

Fabian Furrer, William J. Munro

Published Sep 28, 2018• 63 citations
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Abstract

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.

DOI
10.1103/physreva.98.032335

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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.
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.
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.
We propose a quantum repeater for continuous variable (CV) quantum optical states. Our repeater relies on an error correction protocol for loss on CV states based on CV teleportation and entanglement distillation via noiseless linear amplification. The error correction protocol is concatenated to preserve the same effective transmission coefficient for the quantum channel over increasing distance. The probability of successful operation of the repeater scales polynomially with distance. However, the protocol is limited by a trade-off between fidelity and 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.
A major application of quantum communication is the distribution of entangled particles for use in quantum key distribution. Owing to noise in the communication line, quantum key distribution is, in practice, limited to a distance of a few hundred kilometres, and can only be extended to longer distances by use of a quantum repeater, a device that performs entanglement distillation and quantum teleportation. The existence of noisy entangled states that are undistillable but nevertheless useful for quantum key distribution raises the question of the feasibility of a quantum key repeater, which would work beyond the limits of entanglement distillation, hence possibly tolerating higher noise levels than existing protocols. Here we exhibit fundamental limits on such a device in the form of bounds on the rate at which it may extract secure key. As a consequence, we give examples of states suitable for quantum key distribution but unsuitable for the most general quantum key repeater protocol. Quantum repeaters have been conceived as a means to extend the range of quantum secure communications, but can handle only distillable entangled states. Here, the authors introduce and study quantum key repeaters, devices which may allow long-distance quantum key distribution with non-distillable states.