Jacobi matrices that realize perfect quantum state transfer and early state exclusion

TL;DR

This paper constructs specific 1D Hamiltonians, represented by Jacobi matrices, that enable perfect quantum state transfer and exhibit early state exclusion, with proofs based on special polynomial properties.

Contribution

It introduces a method to design Jacobi matrices for perfect quantum state transfer with early state exclusion, expanding understanding of quantum state dynamics.

Findings

Certain Jacobi matrices achieve perfect quantum state transfer.

Early state exclusion is sometimes impossible with these matrices.

The construction relies on properties of Krawtchouk and Chebyshev polynomials.

Abstract

In this paper we show how to construct 1D Hamiltonians, that is, Jacobi matrices, that realize perfect quantum state transfer and also have the property that the overlap of the time evolved state with the initial state is zero for some time before the transfer time. If the latter takes place we call it an early exclusion state. We also show that in some case early state exclusion is impossible. The proofs rely on properties of Krawtchouk and Chebyshev polynomials.