Entanglement Distribution in a Quantum Network: A Multicommodity Flow-Based Approach

Kaushik Chakraborty,Stephanie Wehner,Bruno Rijsman,David Elkouss

doi:10.1109/tqe.2020.3028172

Kaushik Chakraborty, Stephanie Wehner + Show 2 more

Open Access

https://doi.org/10.1109/tqe.2020.3028172

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Abstract

We consider the problem of optimising 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 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). We also propose an efficient algorithm that takes the output of the linear programming 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 which can achieve those rates.

Highlights

The quantum Internet will provide a facility for communicating qubits between quantum information processing devices [1]–[4]
One might use the linear programming (LP)-formulation corresponding to the standard multicommodity flow-based approach, which we described before, but this would lead to a very loose upper bound on the achievable entanglement generation rate [25]–[32] in this setting
We show that for some classes of practical entanglement generation protocols, one can still have an efficient LP-formulation, which maximizes the total can be understood as repeater r teleporting its qubit entangled with A onto repeater B using the entanglement that it shares with B

Summary

Introduction

The quantum Internet will provide a facility for communicating qubits between quantum information processing devices [1]–[4]. To implement a full quantum internet the network needs to be able to produce entanglement between any two end nodes connected to the network [10]–[13] The performance of such networks will depend on the quantum channels as well as the classical control units [14]. We consider the problem of optimizing the achievable rates for distributing EPR-pairs among multiple source-destination pairs in a network of quantum repeaters while keeping a lower bound on the end-to-end fidelity as a requirement. A source and a destination can be connected via multiple communication channels as well as a sequence of repeaters and each of the communication channels has a certain capacity, which upper bounds the amount of flow it can transmit. A flow must satisfy another restriction, called flow conservation, which says that the amount of flow entering a node (inflow), except the source and destination node, equals

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