Practical repeaters for ultralong-distance quantum communication

Quantum repeaters enable long-range quantum communication in the presence of attenuation. Here we propose a method to construct a robust quantum repeater network using only existing technology. We combine the ideas of brokered graph-state construction with double-heralded entanglement generation to form a system that is able to perform all parts of the procedure in a way that is highly tolerant to photon loss and imperfections in detectors. We show that when used in quantum key distribution this leads to secure kilohertz bit rates over intercontinental distances.

Figure 1

(a)–(e) Illustration of loss-tolerant indirect Bell measurements by brokering. Nuclear spin qubits are in blue and electron spin qubits in green. Red lines represent entanglement connections, which is meant in the sense of an “edge” in a graph state. In particular, the electron qubits are connected together by double heralding in (a) and (b). In (c) these are entangled with the nuclear spins by microwave pulses, and the electron states are measured to give (d). Nuclear spins are then measured to give (e). (f) Four sections of the full repeater protocol, showing S- and R-type repeater stations. Type-S stations send photons to the type-R stations, which entangle one qubit from each side. The R stations then send classical signals back to the S stations, which create their own local entanglement. Local measurements then result in long-range Bell pairs between Alice and Bob.

Figure 2

Secret key rates are shown for various values of inter-repeater distance, $L_0$ (shown in the values next to the different lines), and quality of brokered Bell measurements, $x_{\mathrm{ga}}$. (a), (c) $x_{\mathrm{ga}}=0.95$; (b), (d) $x_{\mathrm{ga}}=0.99$; (a), (b), no distillation; (c), (d), with distillation. Inset: Number of qubit pairs needed to achieve the same rate, $q$, against the proportion of photons on which we postselect, $\mu$.

Figure 3

Attainable secret key rates for different values of brokering quality, $x_{\mathrm{ga}}$, optimized over values of inter-repeater distance $L_0$. Solid lines are without distillation, dashed lines are with. Top, $x_{\mathrm{ga}}=0.999$; middle, $x_{\mathrm{ga}}=0.99$; bottom, $x_{\mathrm{ga}}=0.95$.