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arXiv:2103.11454 · Physical Review A

Improved analytical bounds on delivery times of long-distance entanglement

Tim J. Coopmans, Sebastiaan Brand, David Elkouss

Published Jan 20, 2022• 37 citations
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Abstract

The ability to distribute high-quality entanglement between remote parties is a key element of many quantum network applications, and knowledge of the time at which entanglement is delivered is crucial for assessing the viability of different approaches. In this work, the authors provide improved analytical bounds on the average and on the quantiles of the completion time of entanglement distribution protocols in the case that all network components have success probabilities lower bounded by a constant.

DOI
10.1103/physreva.105.012608

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The ability to distribute high-quality entanglement between remote parties is a key element of many quantum network applications, and knowledge of the time at which entanglement is delivered is crucial for assessing the viability of different approaches. In this work, the authors provide improved analytical bounds on the average and on the quantiles of the completion time of entanglement distribution protocols in the case that all network components have success probabilities lower bounded by a constant.
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Quantum networks enable a number of important applications such as quantum key distribution. The basic function of a quantum network is to enable long-distance quantum entanglement between two remote communication parties. This work focuses on the entanglement routing problem, whose objective is to build long-distance entanglements for the concurrent source-destination pairs through multiple hops. Different from existing works that analyzes the traditional routing techniques on special network topologies, we present a comprehensive entanglement routing model that reflects the differences between quantum networks and classical networks and new entanglement routing algorithms that utilize the unique properties of quantum networks. Evaluation results show that the proposed algorithm Q-CAST increases the number of successful long-distance entanglements by a big margin compared to other methods. The model and simulator developed by this work may encourage more network researchers to study the entanglement routing problem.
End-to-end entanglement distribution is a key capability of upcoming quantum networks, enabling applications like distributed quantum computing, quantum sensor networks, and secure communications. Hence, its realistic and efficient simulation is crucial for quantum network design and for assessing the ability of a network to run certain applications. This work provides tools to scale-up and improve the realism of entanglement generation simulations in quantum networks. This is achieved by deriving analytical results that directly return the success probability, the output state and corresponding fidelity of a selected entanglement generation protocol, while accounting for a variety of noise sources affecting the protocol. These results are then integrated and streamlined in an upgraded version of SeQUeNCe, one of the most popular quantum network simulators. The resulting simulator features increased scalability by reducing computation time by more than 60%, while allowing for a variety of realistic noise sources, including imperfect mode matching, dark counts, and imperfect memory initialization. The simulator is also benchmarked with real experimental data and is capable of replicating the average entanglement generation time and the final state fidelity of a selected experiment. Altogether, the results can enhance current quantum network simulation capabilities towards large-scale networks, paving the way for the future quantum internet.
We develop techniques to analyze the statistics of completion times of nondeterministic elements in quantum-entanglement generation and how they affect the overall performance as measured by the secret key rate. By considering such processes as Markov chains, we show how to obtain exact expressions for the probability distributions over the number of errors that a network acquires, as well as the distribution of entanglement establishment times. We show how results from complex analysis can be used to analyze Markov matrices to extract information with a lower computational complexity than previous methods. We apply these techniques to the Briegel et al. quantum repeater protocol [H.-J. Briegel et al., Phys. Rev. Lett. 81, 5932 (1998)] and find that consideration of the effect of statistical fluctuations can tighten bounds on the secret key rate by three orders of magnitude, when compared to more simplistic analyses. We also use the theory of order statistics to derive tighter bounds on the minimum quantum memory lifetimes that are required in order to communicate securely.