Hamiltonians for one-way quantum repeaters

Filippo M. Miatto1,2, 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

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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.

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.

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