Topological control of quantum speed limits

TL;DR

This paper demonstrates that topological invariants like the Chern number fundamentally bound quantum Fisher information and quantum speed limits, revealing that topological phases can significantly enhance quantum metrology and control.

Contribution

It establishes a direct link between topological invariants and bounds on quantum Fisher information and speed limits, highlighting the role of topology in quantum metrology.

Findings

QFI remains momentum-resolved even in dispersionless states.

Maximum QFI is controlled by topological invariants like the Chern number.

Quantum speed limits scale as the square root of the Chern number in topological phases.

Abstract

Quantum Fisher Information (QFI) is a measure quantifying the sensitivity of a quantum state with respect to changes in tuning parameters in quantum metrology, and defining quantum speed limits. We show that even if the quantum state is completely dispersionless, QFI in this state remains momentum-resolved. We compute the QFI for topological phases at integer filling and demonstrate that each momentum-resolved term is fundamentally bounded by quantum geometric and topological invariants, with maximum QFI controlled by topological invariants (Chern number $|C|$). We also finds bounds on quantum speed limit which scales as $\sqrt{|C|}$ in a (dispersionless) topological phase. We conclude that quantum platforms of high Chern numbers $|C| \gg 1$, such as those featuring twisted multilayered van der Waals heterostructures, significantly enhance capacity for quantum Fisher information, and provide practical control over quantum speed limits.