Implementation of a multi-terminal quantum sorter in solid state systems

Identifying quantum states stands at the core of quantum information processing. However, an accurate observable measurement can pose a tough challenge whenever multiple outcomes are possible, e.g. measuring momentum vs. electron spin, which takes only two components. Quantum systems with a larger number of degrees of freedom increase the options for quantum computations and may enhance the quantum parallelism. Our goal in this work is to define a system that functions as a quantum sorter in a concrete manner, by choosing an interaction Hamiltonian that enables the device to separate the eigenstates into multiple output ports, achieving a so-called mode-lead disentanglement. To this end, we implemented numerically the [Formula: see text]-matrix formalism, which was developed to solve scattering transport problems in solid state systems. The states that are aimed to be separated are described by the transverse momentum of the incident modes and by their spin component, as a possible implementation of qudits. In order to achieve the desired resolution in terms of mode and spin, we study a range of possible Hamiltonians, corresponding to different configurations of the scattering potential.