Nonreciprocity plays a pivotal role in the design of optical and quantum devices. A key mechanism for achieving it lies in the breaking of Lorentz reciprocity. In this paper, we systematically investigate the scattering properties of a non-Hermitian system composed of an arbitrary-dimensional scattering center coupled to two semi-infinite leads. We first propose a general theorem that elucidates how symmetry constrains the transmission and reflection amplitudes. We show that parity-time (PT) symmetric systems can still exhibit reciprocal transmission despite the presence of non-Hermitian terms. The introduction of a magnetic flux that preserves parity symmetry and flux inversion symmetry can break Lorentz reciprocity and thus enable nonreciprocal transport. Based on detailed symmetry analysis, we construct a series of minimal models that demonstrate unidirectional transmission. Our results provide new insights into the mechanisms of nonreciprocal scattering and offer a theoretical foundation for the development of optical diodes and quantum isolators in non-Hermitian systems.
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