Novel categories of electronic devices and quantum materials are obtained by pipelining the unitary evolution of electron quantum states as described by Schroedingers equation with non-unitary processes that interrupt the coherent propagation of electrons. These devices and materials reside in the fascinating transition regime between quantum mechanics and classical physics. The devices are designed such that a nonreciprocal unitary state evolution is achieved by means of a broken inversion symmetry, for example as induced at material interfaces. This coherent state evolution is interrupted by individual inelastic scattering events caused by defects coupled to an environment. Two-terminal non-unitary quantum devices, for example, feature nonreciprocal conductance in linear response. Thus, they are exemptions to Onsagers reciprocal relation, and they challenge the second law of thermodynamics. Implementing the device function into the unit cells of materials or meta-materials yields novel functionalities in 2D and 3D materials, at interfaces, and in heterostructures.
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