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

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.

10 pages, 7 figures

References in corpus (9)

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• Long-distance entanglement and quantum teleportation in XX spin chains
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• Quantum Networks on Cubelike Graphs
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• Quantum Corralling
• Optimally controlled non-adiabatic quantum state transmission in the presence of quantum noise
• State Transfer in Latent-Symmetric Networks
• Pretty Good State Transfer and Minimal Polynomials
• Tailoring quantum walks in integrated photonic lattices
• Control cost and quantum speed limit time in controlled almost exact state transmission in open systems
• Incorporating Encoding into Quantum System Design
• Exact solution of a family of staggered Heisenberg chains with conclusive pretty good quantum state transfer