Time Independence Does Not Limit Information Flow. I. The Free-Particle Case

TL;DR

This paper demonstrates that in long-range free-particle quantum systems, time-independent Hamiltonians can achieve the maximum information transfer speed set by Lieb-Robinson bounds, challenging the notion that time dependence is necessary for optimal transfer.

Contribution

The authors develop and analyze two optimal time-independent quantum state-transfer protocols for free-particle systems with power-law decaying hopping, achieving maximal speed limits.

Findings

Protocols achieve transfer over arbitrary distances with controllable error.

Time independence does not restrict information flow in long-range free-particle systems.

Protocols saturate Lieb-Robinson bounds for free particles.

Abstract

The speed of information propagation in long-range interacting quantum systems is limited by Lieb-Robinson-type bounds, whose tightness can be established by finding specific quantum state-transfer protocols. Previous works have given quantum state-transfer protocols that saturate the corresponding Lieb-Robinson bounds using time-dependent Hamiltonians. Are speed limits for quantum information propagation different for time-independent Hamiltonians? In a step towards addressing this question, we present and analyze two optimal time-independent state-transfer protocols for free-particle systems, which utilize continuous-time single-particle quantum walks with hopping strength decaying as a power law. We rigorously prove and numerically confirm that our protocols achieve quantum state transfer, with controllable error over an arbitrarily long distance in any spatial dimension, at the speed limits set by the free-particle Lieb-Robinson bounds. This shows that time independence does not limit information flow for long-range free-particle Hamiltonians.