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Constant Fidelity Entanglement Flow in Quantum Communication Networks

Tan Bacinoglu, Burhan Gülbahar, Özgür B. Akan

Published Dec 1, 2010• 12 citations
Publisher

Abstract

Entanglement distribution over long distances is one of the main problems in the existing quantum communication networks. Most of the existing methods of establishing entanglement paired link (Einstein, Podolsky, Rosen - EPR pairs) between distant nodes assume symmetric network topologies comprised of links with identical EPR generation capacities. In this work, the entanglement rate capacity of randomly distributed quantum ad hoc networks is investigated. To this end, constant fidelity maximum flow (CFMF) of entanglement problem is defined, and its theoretical analysis is presented. A new heuristic algorithm, i.e., Entanglement Swapping Scheme Search (ESSS), is presented to find the best possible swapping scheme over a multi-hop entanglement path. Furthermore, Shortest Path Entanglement Flow (SPEF) algorithm is introduced as an effective heuristic solution for this problem. Analysis shows that there is a trade-off between the desired constant target fidelity and the entanglement generation rate (maximum flow) of the network.

DOI
10.1109/glocom.2010.5683686

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Entanglement distribution over long distances is one of the main problems in the existing quantum communication networks. Most of the existing methods of establishing entanglement paired link (Einstein, Podolsky, Rosen - EPR pairs) between distant nodes assume symmetric network topologies comprised of links with identical EPR generation capacities. In this work, the entanglement rate capacity of randomly distributed quantum ad hoc networks is investigated. To this end, constant fidelity maximum flow (CFMF) of entanglement problem is defined, and its theoretical analysis is presented. A new heuristic algorithm, i.e., Entanglement Swapping Scheme Search (ESSS), is presented to find the best possible swapping scheme over a multi-hop entanglement path. Furthermore, Shortest Path Entanglement Flow (SPEF) algorithm is introduced as an effective heuristic solution for this problem. Analysis shows that there is a trade-off between the desired constant target fidelity and the entanglement generation rate (maximum flow) of the network.
How to efficiently distribute entanglement over large-scale quantum networks is still an open problem that greatly depends on the technology considered. In this work, we consider quantum networks where each link is characterized by a trade-off between the entanglement generation rate and fidelity. For such networks, we look at the two following problems: the one of finding the best path to connect any two given nodes, and the problem of finding the best starting node in order to connect three nodes in the network multipartite entanglement routing. Two entanglement distribution models are considered: one where entangled qubits are distributed one at a time, and a flow model where a large number of entangled qubits are distributed simultaneously. The paper proposes of a quite general methodology that uses continuous fidelity curves (i.e., entanglement generation fidelity vs. rate) as the main routing metric. Combined with multi-objective path-finding algorithms, the fidelity curves describing each link allow finding a set of paths that maximize both the end-to-end fidelity and the entanglement generation rate. For the link models and networks considered, it is proven that the algorithm always converges to the optimal solution. It is also shown through simulation that the execution time grows polynomially with the number of network nodes (growing with a power between 111 and 1.41.41.4, depending on the network)
We consider the problem of multi-path entanglement distribution to a pair of nodes in a quantum network consisting of devices with non-deterministic entanglement swapping capabilities. Multi-path entanglement distribution enables a network to establish end-to-end entangled links across any number of available paths with pre-established elementary (link-level) entanglement. Probabilistic entanglement swapping, on the other hand, limits the amount of entanglement that is shared between the nodes; this is especially the case when, due to architectural and other practical constraints, swaps must be performed in temporal proximity to each other. Limiting our focus to the case where only bipartite entangled states are generated across the network, we cast the problem as an instance of generalized flow maximization between two quantum end nodes wishing to communicate. We propose a mixed-integer quadratically constrained program (MIQCP) to solve this flow problem for networks with arbitrary topology. We then compute the overall network capacity, defined as the maximum number of EPR states distributed to users per time unit, by solving the flow problem for all possible network states generated by probabilistic entangled link presence and absence, and subsequently by averaging over all network state capacities. The MIQCP can also be applied to networks with multiplexed links – ie, links capable of generating multiple EPR pairs per time unit – by converting the original network state's graph into an equivalent one with unit link capacities. While our approach for computing the overall network capacity has the undesirable property that the total number of states grows exponentially with link multiplexing capability, it nevertheless yields an exact solution that serves as an upper bound comparison basis for the throughput performance of more easily-implementable yet non-optimal entanglement routing algorithms. We apply our capacity computation method to several multiplexed and non-multiplexed networks, including a topology based on SURFnet – a backbone network used for research purposes in the Netherlands – for which real fiber length data is available.
We consider the problem of optimizing the achievable EPR-pair distribution rate between multiple source-destination pairs in a quantum Internet, where the repeaters may perform a probabilistic Bell-state measurement and we may impose a minimum end-to-end fidelity as a requirement. We construct an efficient linear programming (LP) formulation that computes the maximum total achievable entanglement distribution rate, satisfying the end-to-end fidelity constraint in polynomial time (in the number of nodes in the network). Our LP formulation gives the optimal rate for a class of entanglement generation protocols where the repeaters have very short-lived quantum memories. We also propose an efficient algorithm that takes the output of the LP solver as an input and runs in polynomial time (in the number of nodes) to produce the set of paths to be used to achieve the entanglement distribution rate. Moreover, we point out a practical entanglement generation protocol that can achieve those rates.
Entanglement distribution in quantum networks must jointly account for limited link capacities, probabilistic entanglement swapping, and heterogeneous link fidelities. In this paper, we study multi-pair fidelity-aware rate allocation in quantum networks. We formulate three rate-allocation problems: rate sum, rate sum subject to minimum-rate constraints, and max-min fairness. Prior work has studied a special case of the rate sum problem, where all links have identical fidelity. This special case admits a polynomial-time algorithm. We prove that all three problems are NP-hard. We then study optimization versions of these problems which maximize the minimum end-to-end fidelity subject to throughput or fairness requirements. We present fully polynomial-time approximation schemes (FPTAS) for solving these optimization problems. Experiments on randomly generated networks demonstrate the computational effectiveness of the proposed schemes.
Long-distance quantum communication in quantum networks faces significant challenges due to the constraints imposed by the no-cloning theorem. Most existing quantum communication protocols rely on the a priori distribution of entanglement pairs (EPs), a process known to incur considerable latency due to its stochastic nature. In this work, we consider the problem of minimizing the latency of establishing an EP across a pair of nodes in a quantum network. While prior research has primarily focused on minimizing the expected generation latency by selecting static entanglement routes and/or swapping trees in advance, our approach considers a real-time adaptive strategy-wherein the order of entanglement-swapping operations (hence, the swapping tree used) is progressively determined at runtime based on the runtime success/failure of the stochastic events. In this context, we present a greedy algorithm that iteratively determines the best route and/or entanglement-swapping operation to perform at each stage based on the current network. We evaluate our schemes on randomly generated networks and observe a reduction in latency of up to 40% from the optimal offline approach.
Quantum communication technology provides an absolute security guarantee for information transmitted between quantum applications. To establish practical quantum networks, providing entangled pairs of stable quality, suitable for varying distances, is crucial. However, due to the inherent losses and imperfections of the operations during the entanglement distribution process, the fidelity of end-to-end entangled pairs will be greatly reduced. Consequently, establishing fidelity-guaranteed entangled pairs will be challenging. In this work, we introduce an entanglement distribution method that ensures the fidelity requirements of applications across different distances, while maintaining high efficiency. The method first decomposes the end-to-end fidelity requirements to target fidelity for purification at each link, based on the worst-case consumption. Then it performs multiple-round symmetrical entanglement purification based on the backup scheme to purify each entangled pair to the target value. The experimental results indicate that the scheme has acceptable performance in resource consumption and great feasibility while ensuring high efficiency.