Hamiltonians for one-way quantum repeaters

Filippo M. Miatto; Michael Epping; Norbert Lütkenhaus

doi:10.22331/q-2018-07-05-75

Hamiltonians for one-way quantum repeaters

Filippo M. Miatto^1,2, Michael Epping¹, and Norbert Lütkenhaus¹

¹Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, 200 University Ave. W, N2L 3G1 Waterloo, Ontario, Canada
²Télécom ParisTech, LTCI, Université Paris Saclay, 46 Rue Barrault, 75013 Paris, France

Published:	2018-07-05, volume 2, page 75
Eprint:	arXiv:1710.03063v3
Doi:	https://doi.org/10.22331/q-2018-07-05-75
Citation:	Quantum 2, 75 (2018).

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Abstract

Quantum information degrades over distance due to the unavoidable imperfections of the transmission channels, with loss as the leading factor. This simple fact hinders quantum communication, as it relies on propagating quantum systems. A solution to this issue is to introduce quantum repeaters at regular intervals along a lossy channel, to revive the quantum signal. In this work we study unitary one-way quantum repeaters, which do not need to perform measurements and do not require quantum memories, and are therefore considerably simpler than other schemes. We introduce and analyze two methods to construct Hamiltonians that generate a repeater interaction that can beat the fundamental repeaterless key rate bound even in the presence of an additional coupling loss, with signals that contain only a handful of photons. The natural evolution of this work will be to approximate a repeater interaction by combining simple optical elements.

Featured image: One-way quantum repeaters can connect distant endpoints (such as two large cities) with a channel that transports quantum systems reliably. Such technology can enable a global quantum network.

Popular summary

You are reading these words on the screen of your device thanks to a series of contraptions (servers, optical fibres, switches, routers, etc…) that cooperate together to transmit information across the globe unscathed. Among such devices we have repeaters: the light pulses travelling in the optical fibres become exponentially weaker with distance and they need to get beefed up every once in a while. To do so, repeaters measure the feeble signals and re-emit them more strongly.

If instead of classical bits, we wanted to transmit quantum bits of information, we would run into a big problem: we cannot simply measure an unknown quantum system to ''boost it'', because we would inevitably change it and lose the quantum information. To solve this problem, we recall that preserving quantum information is the job of quantum error correcting codes, only here the preservation occurs over space instead of over time. So if we embed our quantum information into bosonic error correcting codes (quantum states of light that slush the quantum information around internally, instead of leaking it), one-way quantum repeaters can fix and re-emit a bosonic code and the quantum information can live on.

In our work, we have linked any bosonic code that we wish to use to the internal Hamiltonian of a quantum repeater, which is the operator that dictates how the device changes the quantum systems that it operates on. In other words, we give a recipe (two recipes actually) to compute the Hamiltonian of a quantum repeater starting from any desired bosonic code. Our hope is one day to find a Hamiltonian that is simple enough to implement using a reasonable number of known quantum optical components.

► BibTeX data

@article{Miatto2018hamiltoniansoneway,
  doi = {10.22331/q-2018-07-05-75},
  url = {https://doi.org/10.22331/q-2018-07-05-75},
  title = {Hamiltonians for one-way quantum repeaters},
  author = {Miatto, Filippo M. and Epping, Michael and L{\"{u}}tkenhaus, Norbert},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {75},
  month = jul,
  year = {2018}
}

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Cited by

[1] Filip Rozpędek, Kyungjoo Noh, Qian Xu, Saikat Guha, and Liang Jiang, "Quantum repeaters based on concatenated bosonic and discrete-variable quantum codes", npj Quantum Information 7 1, 102 (2021).

[2] Gregory R. Steinbrecher, Jonathan P. Olson, Dirk Englund, and Jacques Carolan, "Quantum optical neural networks", npj Quantum Information 5 1, 60 (2019).

[3] Sumeet Khatri, "Policies for elementary links in a quantum network", Quantum 5, 537 (2021).

[4] Sumeet Khatri, Corey T. Matyas, Aliza U. Siddiqui, and Jonathan P. Dowling, "Practical figures of merit and thresholds for entanglement distribution in quantum networks", Physical Review Research 1 2, 023032 (2019).

[5] Jiangyuan Yao, Kaiwen Zou, Deshun Li, and Zheng Jiang, 2021 IEEE 23rd Int Conf on High Performance Computing & Communications; 7th Int Conf on Data Science & Systems; 19th Int Conf on Smart City; 7th Int Conf on Dependability in Sensor, Cloud & Big Data Systems & Application (HPCC/DSS/SmartCity/DependSys) 361 (2021) ISBN:978-1-6654-9457-1.

[6] Wim Bogaerts, Daniel Pérez, José Capmany, David A. B. Miller, Joyce Poon, Dirk Englund, Francesco Morichetti, and Andrea Melloni, "Programmable photonic circuits", Nature 586 7828, 207 (2020).

[7] Sumeet Khatri, "On the design and analysis of near-term quantum network protocols using Markov decision processes", AVS Quantum Science 4 3, 030501 (2022).

[8] Siddhartha Das, Sumeet Khatri, and Jonathan P. Dowling, "Robust quantum network architectures and topologies for entanglement distribution", Physical Review A 97 1, 012335 (2018).

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