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arXiv:2406.13492 · Physical Review A

Multipartite multiplexing strategies for quantum routers

Julia Kunzelmann, Hermann Kampermann, Dagmar Bruß

Published Sep 18, 2024• 2 citations
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Abstract

This work explores the important role of quantum routers in communication networks and investigates the increase in efficiency using memories and multiplexing strategies. Motivated by the bipartite setup introduced by Abruzzo et al. [Phys. Rev. A 89, 012303 (2014)] for finite-range multiplexing in quantum repeaters, we extend the study to an $N$-partite network with a router as a central station. We present a general protocol for $N$ parties after defining the underlying matching problem and we calculate the router rate for different $N$. We analyze the improvement due to multiplexing and analyze the secret key rate with explicit results for the tripartite network. Investigating strategic qubit selection for the Greenberger-Horne-Zeilinger measurements, we show that using cutoffs to remove qubits after a certain number of rounds and consistently combining qubits with the lowest number of storage rounds leads to an optimal secret key rate.

DOI
10.1103/physreva.110.032617

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This work explores the important role of quantum routers in communication networks and investigates the increase in efficiency using memories and multiplexing strategies. Motivated by the bipartite setup introduced by Abruzzo et al. [Phys. Rev. A 89, 012303 (2014)] for finite-range multiplexing in quantum repeaters, we extend the study to an NNN-partite network with a router as a central station. We present a general protocol for NNN parties after defining the underlying matching problem and we calculate the router rate for different NNN. We analyze the improvement due to multiplexing and analyze the secret key rate with explicit results for the tripartite network. Investigating strategic qubit selection for the Greenberger-Horne-Zeilinger measurements, we show that using cutoffs to remove qubits after a certain number of rounds and consistently combining qubits with the lowest number of storage rounds leads to an optimal secret key rate.
Over the past few years, the concept of quantum routers and their usefulness in quantum communication networks (e.g., in the BB84 protocol [5]) has been popularized in quantum information theory. While quite some work has been done on the theoretical implementation of quantum routers using multiplexing, most of it is constrained to the bipartite case [2, 9]. We extend this setup to quantum routers used in multipartite conference key agreement protocols so as to distribute a secret key among N parties. We formalize the general quantum entanglement matching problem, and show it's NP-completeness. We then study special cases for which we found efficient algorithms. Finally, we consider the weighted case where the weights represent the qubit ages.
Quantum repeaters represent one possible way to achieve long-distance quantum key distribution. Collins et al. [O. A. Collins, S. D. Jenkins, A. Kuzmich, and T. A. B. Kennedy, Phys. Rev. Lett. 98, 060502 (2007)] proposed multiplexing as a method to increase the repeater rate and to decrease the requirement of memory coherence time. Motivated by the experimental fact that long-range connections are practically demanding, in this paper we extend the original quantum repeater multiplexing protocol to the case of short-range connection. We derive analytical formulas for the repeater rate and we show that for short connection lengths it is possible to have most of the benefits of a full-range multiplexing protocol. Then we incorporate decoherence of quantum memories and we study the optimal matching for the Bell-state measurement protocol permitting us to minimize the memory requirements. Finally, we calculate the secret key rate and we show that the improvement via finite-range multiplexing is of the same order of magnitude as that via full-range multiplexing.
We consider a multiplexed quantum repeater that distributes entanglement between two end nodes. Multiplexing is achieved through optical integration of many quantum chips. Each chip hosts an optically addressable communication qubit and a separate memory qubit. The communication qubit serves as an entanglement generation interface between different quantum chips, and the memory qubit can be used to store entanglement. The quantum chips on the repeater are interconnected using a reconfigurable router, which makes it possible to dynamically assign quantum chips for entanglement generation with either of the two end nodes in every end-to-end communication cycle. We propose a dynamic multiplexing policy in which after an entangled link has been established with one of the end nodes, all remaining quantum chips are assigned to the opposite end node. We compare this dynamic policy to a policy in which the assignment of quantum chips to end nodes is fixed. We consider a parameter regime where on average less than one entangled link is generated per end-to-end communication cycle, which is the relevant regime for near-term quantum networks. We show that in this regime, the dynamic multiplexing policy can lead to a significant improvement in fidelity over a fixed policy, while marginally improving the rate. Moreover, even though the dynamic multiplexing policy requires a deeper, and hence, more lossy, router than the fixed policy, it can still achieve higher secret key rates in the parameter regime studied. This makes dynamic multiplexing with a many-quantum-chip repeater especially relevant for the development of near-term quantum networks.
Quantum communication enables the implementation of tasks that are unachievable with classical resources. However, losses on the communication channel preclude the direct long-distance transmission of quantum information in many relevant scenarios. In principle, quantum repeaters allow one to overcome losses. However, realistic hardware parameters make long-distance quantum communication a challenge in practice. For instance, in many protocols an entangled pair is generated that needs to wait in quantum memory until the generation of an additional pair. During this waiting time the first pair decoheres, impacting the quality of the final entanglement produced. At the cost of a lower rate, this effect can be mitigated by imposing a cutoff condition. For instance, a maximum storage time for entanglement after which it is discarded. In this article, we optimize the cutoffs for quantum repeater chains. First, we develop an algorithm for computing the probability distribution of the waiting time and fidelity of entanglement produced by repeater chain protocols which include a cutoff. Then, we use the algorithm to optimize cutoffs in order to maximize the secret-key rate between the end nodes of the repeater chain. In this article, we find that the use of the optimal cutoff extends the parameter regime for which secret key can be generated and, moreover, significantly increases the secret-key rate for a large range of parameters.
The distribution of entangled states is a core task for quantum networks facilitating quantum communication, and the use of multipartite entangled states comes with its own set of considerations. In this work, we analyze a quantum conference agreement protocol based on GHZ states in a network with a central station to which multiple clients are connected. Using comprehensive numerical simulations, we investigate how minor variations in the scenario-such as the number of parties, the number of memories, and asymmetric distances from the central station-can drastically influence the performance of the protocol. In particular, we demonstrate that it is crucial to adjust the strategy by optimizing cutoff times. From a broader perspective, we argue that numerical simulations are an indispensable tool for protocol design for devising realistic schemes for quantum communication.