Parameter estimation with the steady states of non-Hermitian spin chains

We propose a scheme for parameter estimation with the steady states of non-Hermitian spin chains. The parameters to be estimated are encoded in the system via the external magnetic field that imposed on the first site of the chain. We obtain the analytical spectrum for the spin chain of two sites. We find that the quantum Fisher information (QFI) about the amplitude of the imposing field diverges while the QFI about the azimuthal angle reaches to the maximum at exceptional points. Moreover, the QFI is enhanced as the system size increasing and saturates for sufficiently long spin chain because only short-range correlations are induced by the imposing field.

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