State Transfer in Highly Connected Networks and a Quantum Babinet Principle

TL;DR

This paper explores quantum state transfer in highly connected two-dimensional networks, revealing conditions for perfect transfer and introducing a quantum Babinet principle relating complementary network structures.

Contribution

It introduces a quantum Babinet principle and identifies network structures that enable perfect quantum state transfer.

Findings

Perfect state transfer occurs in N/2-cross polytope graphs when N is divisible by 4.

A quantum Babinet principle relates complementary graphs with identical transfer fidelity.

The principle generalizes classical optics concepts to quantum network design.

Abstract

The transfer of a quantum state between distant nodes in two-dimensional networks, is considered. The fidelity of state transfer is calculated as a function of the number of interactions in networks that are described by regular graphs. It is shown that perfect state transfer is achieved in a network of size N, whose structure is that of a N/2-cross polytope graph, if N is a multiple of 4. The result is reminiscent of the Babinet principle of classical optics. A quantum Babinet principle is derived, which allows for the identification of complementary graphs leading to the same fidelity of state transfer, in analogy with complementary screens providing identical diffraction patterns.