Braess Paradox in a quantum network

TL;DR

This paper demonstrates a quantum analogue of the Braess paradox, showing that adding an entangled link to a quantum network can decrease the entanglement between two nodes, counterintuitive to classical network behavior.

Contribution

It introduces the concept of the Braess paradox in quantum networks, revealing that adding entanglement links can reduce overall entanglement between nodes.

Findings

Adding a maximally entangled edge reduces concurrence between nodes

Quantum Braess paradox occurs in entanglement distribution networks

Counterintuitive impact of network augmentation on quantum correlations

Abstract

Dietrich Braess while working on traffic modelling, noticed that traffic flow in a network can be worsened by adding extra edges to an existing network. This seemingly counterintuitive phenomenon is known as the Braess paradox. We consider a quantum network, where edges represent shared entangled states between spatially separated parties(nodes). The goal is to entangle two previously uncorrelated nodes using entanglement swappings. The amount of entanglement between the distant nodes is quantified by the average concurrence of the states established, as a result of the entanglement swappings. We then introduce an additional edge of maximally entangled Bell states in the network. We show that the introduction of the additional maximally entangled states to this network leads to lower concurrence between the two previously un-correlated nodes. Thus we demonstrate the occurrence of a phenomenon in a quantum network that is analogous to the Braess' paradox in traffic networks.