Almost perfect state transfer in quantum spin chains

TL;DR

This paper investigates almost perfect state transfer (APST) in quantum spin chains, showing it occurs under less restrictive conditions than perfect transfer, with implications for efficient quantum communication.

Contribution

It demonstrates that APST occurs in mirror-symmetric XX spin chains when 1-excitation energies are linearly independent over rationals, expanding understanding of quantum state transfer conditions.

Findings

APST occurs in mirror-symmetric systems.

APST requires less restrictive conditions than PST.

APST accommodates imperfections in quantum chains.

Abstract

The natural notion of almost perfect state transfer (APST) is examined. It is applied to the modelling of efficient quantum wires with the help of $XX$ spin chains. It is shown that APST occurs in mirror-symmetric systems, when the 1-excitation energies of the chains are linearly independent over rational numbers. This result is obtained as a corollary of the Kronecker theorem in Diophantine approximation. APST happens under much less restrictive conditions than perfect state transfer (PST) and moreover accommodates the unavoidable imperfections. Some examples are discussed.