Topological protection of local quantum Fisher information

TL;DR

This paper demonstrates that topological phases in quantum systems can protect local quantum Fisher information from dispersal, enabling robust quantum metrology at the boundaries of a Kitaev chain.

Contribution

It analytically shows how topological boundary modes preserve quantum Fisher information, with exact formulas and numerical evidence of robustness against disorder and interactions.

Findings

Majorana zero modes fix boundary QFI at a nonzero plateau

Spatial separation of Majorana quadratures causes boundary memory

Boundary plateau persists under moderate disorder and interactions

Abstract

In many-body quantum systems, unitary dynamics generically delocalize locally encoded information, causing single-site metrological sensitivity to vanish. We analytically demonstrate that a topological phase can prevent this dispersal. In the open Kitaev chain, a Majorana zero mode fixes the boundary quantum Fisher information (QFI) at a nonzero plateau that persists for times exponentially long in system size. We derive exact analytical expressions for the local QFI and identify the mechanism as the spatial separation of the two Majorana quadratures to opposite ends of the chain. This separation produces a boundary encoding-axis asymmetry that distinguishes topological boundary memory from a generic localized subgap signal. We show numerically that the asymmetry is robust to moderate quenched on-site disorder, while the boundary plateau remains visible under parity-preserving interactions in finite-size real-time simulations. The protocol requires only product-state initialization, Hamiltonian evolution, and single-site readout.