Quantum network reliability with perfect nodes

TL;DR

This paper introduces quantum reliability and a related operator, extending classical network reliability concepts to quantum networks, and presents a Negami-like splitting formula addressing quantum entanglement challenges.

Contribution

It defines quantum reliability and the quantum reliability operator, providing a novel splitting formula that accounts for quantum entanglement effects.

Findings

Quantum reliability operator is introduced and related to network reliability.

A Negami-like splitting formula for quantum reliability is derived.

Classical factorization does not hold in quantum networks due to entanglement.

Abstract

We introduce the concept of quantum reliability as an extension of the concept of network reliability in the context of quantum networks. We show that this concept is intimately related to the concept of quantum reliability operator that we also introduce and show a Negami like splitting formula for it. Considering that the simple factorization formula for classical networks which is the basis of most of the calculation algorithms does not hold in the quantum context due to entanglement, a Negami like splitting for the quantum reliability operator becomes relevant.