Deterministic Entanglement Distribution on Series-Parallel Quantum Networks

TL;DR

This paper introduces a deterministic entanglement distribution scheme based on concurrence percolation theory, which improves scalability and success probability over classical methods in quantum networks, with practical implementation on IBM quantum hardware.

Contribution

It develops a new mathematical framework for deterministic entanglement distribution applicable to arbitrary quantum network topologies, surpassing classical percolation schemes.

Findings

DET scheme outperforms nested repeater protocol in entanglement distillation.

Higher success probabilities for maximally entangled states compared to CEP.

Experimental validation on IBM quantum platform confirms feasibility.

Abstract

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topologies. More precisely, we implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary d-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized k-concurrences (a family of fundamental entanglement measures) for different QN topology. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform.