Asymptotically perfect efficient quantum state transfer across uniform chains with two impurities

TL;DR

This paper demonstrates that adding impurities at the ends of a uniform quantum chain enables high-fidelity, asymptotically perfect quantum state transfer with a polynomial time scaling, eliminating the need for external control.

Contribution

The work introduces a method to achieve near-perfect quantum state transfer in uniform chains by tuning impurities, significantly improving transfer efficiency without external control.

Findings

State transfer time scales as N^{3/2}

Fidelity approaches 1 as N approaches infinity

Error scales as 1/N

Abstract

The ability to transfer quantum information from one location to another with high fidelity is of central importance to quantum information science. Unfortunately for the simplest system of a uniform chain (a spin chain or a particle in a one-dimensional lattice), the state transfer time grows exponentially in the chain length $N$ at fixed fidelity. In this work we show that the addition of an impurity near each endpoint, coupled to the uniform chain with strength $w$, is sufficient to ensure efficient and high-fidelity state transfer. An eigenstate localized in the vicinity of the impurity can be tuned into resonance with chain extended states by tuning $w(N)\propto N^{1/2}$; the resulting avoided crossing yields resonant eigenstates with large amplitudes on the chain endpoints and approximately equidistant eigenvalues. The state transfer time scales as $t\propto N^{3/2}$ and its fidelity $F$ approaches unity in the thermodynamic limit $N\to\infty$; the error scales as $1-F\propto N^{-1}$. Thus, with the addition of two impurities, asymptotically perfect state transfer with a uniform chain is possible even in the absence of external control.