Interplay between speed and fidelity in off-resonant quantum-state-transfer protocols

Abstract

An arbitrary qubit can be transmitted through a spin chain by perturbatively coupling both communicating parties to it. These so-called weak-coupling models rely on effective Rabi oscillations between the outer spins, yielding nearly maximum fidelity while offering great resilience against disorder with the cost of having long transfer times. Considering that framework, here we address a one-dimensional nonsymmetric channel connecting two spins, one placed at each end of it. Given any pattern of nearest-neighbor coupling strengths, we obtain an analytical expression that accounts for the effective long-range interaction between them and study the interplay between transfer time and fidelity. Furthermore, we show that homogeneous channels provide the best speed-fidelity tradeoff.