Multiplexed Memory-Insensitive Quantum Repeaters

Long-distance quantum communication via distant pairs of entangled quantum bits (qubits) is the first step towards secure message transmission and distributed quantum computing. To date, the most promising proposals require quantum repeaters to mitigate the exponential decrease in communication rate due to optical fiber losses. However, these are exquisitely sensitive to the lifetimes of their memory elements. We propose a multiplexing of quantum nodes that should enable the construction of quantum networks that are largely insensitive to the coherence times of the quantum memory elements.

Figure 1

(a) Processes of an $N=3$ multiplexed quantum repeater. In addition to two terminal nodes, the network has seven internal nodes consisting of two quantum memory sites containing $n$ independent memory elements. Entanglement generation proceeds with probability $P_0$, creating 8 entanglement lengths of $L_0$. In the lowest panel, shaded memory sites indicate successfully entangled segments. The $N=1$ level entanglement connection proceeds with probability $P_1$, producing four entangled segments of length $2L_0$. Nodes reset to their vacuum states by the connection are blank. The $N=2$ and $N=3$ levels proceed with probabilities $P_2$ and $P_3$. Each stage results in entanglement-length doubling, until an $N=3$ success entangles the terminal nodes. (b) and (c) show the topology of the $n$ memory element sets. The parallel architecture (b) connects entanglement only between memory elements with the same address. In contrast, multiplexing (c) uses a fast sequential scanning of all memory element addresses to connect any available memory elements.

Figure 2

Plot of $⟨T{⟩}_{\tau }$ against $\tau$. $P_0=0.01$, $P_1=0.5$. The minimum possible success time of 2 imposes a similar minimum of the on quantum memory element lifetimes.

Figure 3

Comparison of entanglement connection rate $f_{\tau }$ for parallel (dashed line) and multiplexed (solid line) architectures as a function of coherence time. $P_0=0.01$, $P_1=0.1$. (a) Solid circles denote simulated values for the multiplexed case. (b) Parallel repeaters of any $n$ value follow the $n=1$ line. As $n$ increases, multiplexed scaling improves while parallel scaling remains constant.

Figure 4

Simulated entanglement distribution over 1000 km for multiplexed (solid line) and parallel (dashed line) $N=3$ quantum repeaters. For $\tau \ge 100\mathrm{msec}$, the multiplexed distribution rate is almost flat for $n\gtrsim 10$; parallel rates decrease by 2 orders of magnitude. For low memories a multiplexed $n=10$ repeater outperforms an $n=1000$ parallelization.