Quantum Metrology in Anti‐PT‐Symmetric Systems

ABSTRACT Non‐Hermitian systems have attracted increasing attention in recent years, particularly those exhibiting Parity‐Time (PT) symmetry. Quantum metrology establishes the ultimate attainable bounds for parameter estimation in both Hermitian and non‐Hermitian systems. However, comparatively little is known about non‐Hermitian systems with anti‐Parity‐Time (APT) symmetry. In this work, we investigate the theoretical bounds on quantum parameter estimation precision for an APT‐symmetric system governed by the Bogoliubov–de Gennes (BdG) Hamiltonian. We explicitly derive the expression for the quantum Fisher information (QFI) and compare the attainable precision limits for both multiplicative and non‐multiplicative parameters in the BdG Hamiltonian. Our analysis of the effective QFI reveals that quantum parameter estimation precision can be significantly enhanced as the system approaches the exceptional point with unbroken APT symmetry, where Heisenberg scaling becomes achievable. We also examine how the effective QFI depends on the choice of initial states. Furthermore, we demonstrate that entanglement in multi‐particle initial state can provide an additional enhancement to the QFI. The ratio of limit of parameter estimation precision of the entangled state to the greatest one we have found over all the tensor product states is 1.22, which is greater than 1. Our analysis of two‐particle states confirms that entanglement in the initial state can further increase the QFI, highlighting it as a valuable quantum resource. These findings lay a theoretical foundation for future experimental explorations of parameter estimation in APT‐symmetric non‐Hermitian systems.