Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains

Abstract

Quantum communication enables a host of applications that cannot be achieved by classical communication means, with provably secure communication as one of the prime examples. The distance that quantum communication schemes can cover via direct communication is fundamentally limited by losses on the communication channel. By means of quantum repeaters, the reach of these schemes can be extended and chains of quantum repeaters could in principle cover arbitrarily long distances. In this work, we provide two efficient algorithms for determining the generation time and fidelity of the first generated entangled pair between the end nodes of a quantum repeater chain. The runtime of the algorithms increases polynomially with the number of segments of the chain, which improves upon the exponential runtime of existing algorithms. Our first algorithm is probabilistic and can analyze refined versions of repeater chain protocols which include intermediate entanglement distillation. Our second algorithm computes the waiting time distribution up to a pre-specified truncation time, has faster runtime than the first one and is moreover exact up to machine precision. Using our proof-of-principle implementation, we are able to analyze repeater chains of thousands of segments for some parameter regimes. The algorithms thus serve as useful tools for the analysis of large quantum repeater chain protocols and topologies of the future quantum internet.

Improved analytical bounds on delivery times of long-distance entanglement

“…For many schemes, the completion time is complex to express due to feedback loops and restarts. Although numerically progress has recently been made in determining the completion time for increasingly larger networks [15,[21][22][23][24][25], numerical approaches provide only limited intuition and moreover are demanding in computation time when performing largescale optimization over many network designs and hardware parameters. For this reason, analytical results are more convenient.…”

“…Neither approximation is ideal, since some success probabilities can be boosted by techniques such as multiplexing, while others are bounded well below 1 for some setups [34]. Indeed, numerics have shown for some of the approximations that they become increasingly bad as the size of the network grows [22,23]. Another scenario in which the completion time probability distribution is brought back to a known form includes the discarding of entanglement [35,36].…”

Policies for elementary links in a quantum network

“…One of the goals of this work is to explicitly formalize the approaches taken in the aforementioned works within the context of decision processes, because this allows us to systematically study different policies and calculate quantities that are relevant for quantum networks, such as entanglement distribution rates and fidelities of the quantum states of the links. This work is complementary to prior work that uses Markov chains to analyze waiting times and entanglement distribution rates for a chain of quantum repeaters [65,[130][131][132]; we also refer to the work on entanglement switches in [80][81][82][83], which use both discrete-time and continuous-time Markov chains. This work is also complementary to prior work that analyzes the quantum state in a quantum repeater chain with noisy quantum memories [133][134][135][136][137].…”

Designing a quantum network protocol

“…Repeater chain protocols Since many long-distance links in the quantum internet will be built by chaining many quantum repeaters, protocols for such constructions have received significant attention [9,10,18,29,31,37,49,58,71,73,75,76,86]. However, these protocols are limited in scope to individual chains: they cannot handle non-linear topologies and do not have mechanisms for merging and splitting flows.…”