Fault-Tolerant Quantum Communication Based on Solid-State Photon Emitters

We describe a novel protocol for a quantum repeater that enables long-distance quantum communication through realistic, lossy photonic channels. Contrary to previous proposals, our protocol incorporates active purification of arbitrary errors at each step of the protocol using only two qubits at each repeater station. Because of these minimal physical requirements, the present protocol can be realized in simple physical systems such as solid-state single photon emitters. As an example, we show how nitrogen-vacancy color centers in diamond can be used to implement the protocol, using the nuclear and electronic spin to form the two qubits.

Figure 1

Protocol for fault-tolerant quantum communication. Each node is represented by an oval containing two qubits (circles). Entangled states are represented by a solid or a dashed line between the entangled qubits. (a) Entanglement connection. (b) Nested entanglement purification. Dots indicate an arbitrary number of nodes.

Figure 2

(a) Fidelity scaling with distance. Points show results using 3 purification steps at each nesting level; dashed lines show the fixed point $F_{FP}$ at each distance; dotted lines indicate the asymptotic fidelity $F_{\infty }$. For (a) and (b), measurements and local two-qubit operations $\eta =p$ contain 0.5% errors. For (a), (b), and (c), the initial fidelity $F_0$ is (i) 100%, (ii) 99%, (iii) 98%, (iv) 97%, (v) 96% with phase errors only. (b) Time scaling with distance for $m=3$, given in units of $T_0\gg L_0/c$, the time required to generate entanglement between nearest neighbors, and $L_0$, the distance between nearest neighbors. (c) Long-distance asymptote dependence on operation and measurement errors. (d) Long-distance asymptote dependence on error type ($F_0=0.99$, $\upsilon =0,0.1,0.2,0.3$).

Figure 3

(a) Interferometric arrangement for entanglement generation. Inset shows relevant level scheme. (b) Implementation with NV centers. Electronic spin ($|0⟩,|1⟩$) and ${}^{13}\mathrm{C}$ nuclear spin ($|\uparrow ⟩,|\downarrow ⟩$) states are coupled by optical, microwave, and rf transitions. The $M_s=-1$ electronic state can be shifted out of resonance by a small magnetic field.