Hermitian systems possess unitary scattering.However,the Hermiticity is unnecessary for a unitary scattering although the scattering under the influence of non-Hermiticity is mostly non-unitary.Here we prove that the unitary scattering is protected by certain type of pseudo-Hermiticity and unaffected by the degree of non-Hermiticity.The energy conservation is violated in the scattering process and recovers after scattering.The subsystem of the pseudo-Hermitian scattering center including only the connection sites is Hermitian.These findings provide fundamental insights on the unitary scattering,pseudo-Hermiticity,and energy conservation,and are promising for light propagation,mesoscopic electron transport,and quantum interference in non-Hermitian systems.
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