Tunable topological enhancement of covariant quantum Fisher information via non-Bloch skin effect in non-Hermitian SSH lattices

Abstract

The covariant quantum Fisher information (CQFI) has recently been established as the ultimate precision benchmark for pseudo-Hermitian sensors [Phys. Rev. Lett. 136, 080802 (2026)], yet existing analyses are limited to single-mode systems. Here we extend the CQFI formalism to multi-mode non-Hermitian Su-Schrieffer-Heeger lattices and reveal tunable topological enhancement enabled by the non-Hermitian skin effect (NHSE). Under open boundary conditions, the NHSE deforms the conventional Brillouin zone into a generalized Brillouin zone of radius r = exp(\k{appa}), where \k{appa} denotes the non-Bloch decay rate. While the total CQFI scales linearly with system size N, its prefactor depends critically on \k{appa}, yielding an enhancement factor E(N) = F_OBC / F_PBC that exceeds 30 for N ~ 30, substantially outperforming periodic-boundary sensors. The enhancement is robust against moderate local disorder and supports multi-parameter estimation, with the joint Cramér-Rao bound reduced by up to 15 orders of magnitude. These findings establish a spatial-domain mechanism for quantum metrology that complements time-domain strategies and is experimentally accessible using topoelectrical circuits, photonic lattices, and superconducting circuits with current technology.