Long-distance quantum communication sending single photons and keeping many

Abstract

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.

Figures (7)

• Figure 1: (Color online) Sketch of the all-optical memory: 1 The encoded (yellow) half of the hybrid entangled state of Eq. (\ref{['eq::hybridstate']}) is coupled into the fiber loop for storage, while the dual-rail qubit travels through the fiber towards the segment midpoint. 2 During the wait time, intermediate corrections are applied via a Bell-state measurement (BSM) together with a fresh encoded Bell pair, 3 after which the Bell pair's other component is coupled back into the loop. 4 Upon receiving the signal heralding distribution success in the adjoining segment to the left, the state is directed towards a second BSM device, where it is combined with the state stored in the station's other memory for entanglement swapping.
• Figure 2: (Color online) Use of basic resources for the Steane-GKP protocol: Six GKP Bell pairs Walshe2020 are converted by a passive linear-optics setup into a GKP Steane-GKP hybrid cubecreation. States of this type can be used to create the entangled states used in the repeater scheme. Seven GKP BSMs provide the full Steane-GKP syndrome information Schmidt2022.
• Figure 3: (Color online) SKF of Steane-GKP repeater as a function of loop and segment number, $m$ and $n$, respectively. Operating in the long-segment regime is possible with enough intermediate corrections. Parameters: $L=1000$km, $s=15$dB, $p_\text{link}=p_\text{loop}=0.99$. Pauli errors during state preparation are included in the SKF.
• Figure 4: (Color online) (a) Squeezing demands of regular GKP and Steane-GKP codes for different total lengths. (b) Secret key fractions as a function of total distance for various protocols. Parameters: $n=100$, $p_\text{link}=p_\text{loop}=0.99$, $m$ optimized. Plots for Steane-GKP include the effect of Pauli errors during state preparation.
• Figure 5: (Color online) Error correction of Gaussian shifts. The graph shows the distribution of the true shift, the dashed lines separate shaded regions where the syndrome interpretation leads to a logical error from those where no error occurs.