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Long distance quantum communication using quantum error correction

Robert M. Gingrich, Hwang Lee, Jonathan P. Dowling

Published Jan 5, 2004• 0 citations
Publisher

Abstract

Currently long distance quantum communication is limited by the photon loss. We describe a quantum error correction scheme that can increase the effective absorption length of the communication channel. This device can play the role of a quantum transponder when placed in series, or a cyclic quantum memory when inserted in an optical loop.

DOI
10.5555/984720.984758

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Currently long distance quantum communication is limited by the photon loss. We describe a quantum error correction scheme that can increase the effective absorption length of the communication channel. This device can play the role of a quantum transponder when placed in series, or a cyclic quantum memory when inserted in an optical loop.
When photons are sent through a fiber as part of a quantum communication protocol, the error that is most difficult to correct is photon loss. Here we propose and analyze a two-to-four qubit encoding scheme, which can recover the loss of one qubit in the transmission. This device acts as a repeater, when it is placed in series to cover a distance larger than the attenuation length of the fiber, and it acts as an optical quantum memory, when it is inserted in a fiber loop. We call this dual-purpose device a "quantum transponder."
Fiber-based classical communication is all-optical and uses light pulses reamplified and reshaped every 50-100 km in classical repeaters. Most compatible with this would be a quantum communication system which is also all-optical with quantum processing units placed in similar intervals. However, existing all-optical quantum communication protocols either require complicated quantum error correction steps for logical-qubit recoveries at every few kilometers or, over larger quantum repeater segments, they would at least depend on sharing complex multi-photon entangled states. Here we propose an all-optical memory-based quantum repeater for long-distance quantum communication, with quantum memories at each repeater station realized in the form of fiber loops combined with suitable quantum error correction codes for photon-loss protection. By sending only single-photon states through the fibers connecting the stations, such repeaters can operate in the classical infrastructure's long-segment regime. We analyze the performance of our scheme for the Gottesman-Kitaev-Preskill code, including a concatenation with the Steane code, as well as the single-photon quantum parity code for total distances up to 10000 km.
Long-distance quantum communication with high fidelity is the main obstacle to creating a quantum network. A scheme to recover the loss of one photon with a three-to-eight qubit encoding is presented. The qubit loss is first detected using a quantum nondemolition measurement and is then transformed into a standard qubit error by inserting a new photon. The state of qubits is reconstructed via a sequence of one projective measurement, two single-qubit gates, and seven controlled-NOT operations. No ancillary qubits are required. Finally, the cost of resources is analyzed.
This study develops a method to overcome the effect of loss in optical fibers, which is one of the main obstacles to long-distance quantum communication. The work discusses an architecture for quantum repeaters, in which information is encoded in error-correcting codes capable of handling both photon loss and logical errors. Advantages of this approach are that it can work with very limited resources at each repeater station, and is more robust to errors than previous techniques. The results can promote long-distance quantum communication at very high rates.
Abstract: This chapter explores the engineering of quantum repeaters, a critical technology for enabling secure and scalable long-distance quantum communication. Quantum repeaters extend the range of quantum communication networks by preserving entanglement and mitigating signal loss over large distances. The chapter covers the key principles of entanglement swapping, quantum memory, and quantum error correction, which are essential for maintaining the integrity of quantum states. It also examines advanced repeater architectures, including multi-mode repeaters and entanglement purification techniques, to improve scalability and robustness. Case studies highlight real-world implementations of quantum repeaters in quantum key distribution (QKD) networks, demonstrating their role in achieving secure global communication. Keywords: quantum repeaters, long-distance quantum communication, entanglement swapping, quantum memory, quantum error correction, entanglement purification, multi-mode repeaters, quantum key distribution, QKD, scalable quantum networks, secure communication.