Optimal path for a quantum teleportation protocol in entangled networks

TL;DR

This paper reveals that Bellman's optimality principle does not hold in quantum teleportation networks, indicating that optimizing quantum state transfer fidelity is a complex problem requiring new approaches.

Contribution

It demonstrates the violation of Bellman's principle in quantum networks, highlighting the need for novel methods to optimize quantum teleportation.

Findings

Bellman's principle is violated in quantum teleportation networks

Optimal fidelity routing in quantum networks is a complex problem

Further research is needed for effective optimization methods

Abstract

Bellman's optimality principle has been of enormous importance in the development of whole branches of applied mathematics, computer science, optimal control theory, economics, decision making, and classical physics. Examples are numerous: dynamic programming, Markov chains, stochastic dynamics, calculus of variations, and the brachistochrone problem. Here we show that Bellman's optimality principle is violated in a teleportation problem on a quantum network. This implies that finding the optimal fidelity route for teleporting a quantum state between two distant nodes on a quantum network with bi-partite entanglement will be a tough problem and will require further investigation.