@misc{PredaGhiuIonetal., author = {Preda, Amanda Teodora and Ghiu, Iulia and Ion, Lucian and Wulf, Ulrich and Manolescu, Andrei and Nemnes, George Alexandru}, title = {Implementation of a multi-terminal quantum sorter in solid state systems}, series = {Scientific reports}, volume = {15}, journal = {Scientific reports}, number = {1}, publisher = {Nature Publishing Group UK}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-025-05860-x}, pages = {1 -- 12}, abstract = {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 -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.}, language = {en} } @misc{KučeraWulfNemnes, author = {Kučera, Jan and Wulf, Ulrich and Nemnes, George Alexandru}, title = {Scattering theory in an N-pole semiconductor quantum device : the unitarity of the current S-matrix and current conservation}, series = {Micromachines}, volume = {16}, journal = {Micromachines}, number = {3}, editor = {Xue, Junshuai and Jiang, Xi and Yuan, Song}, publisher = {MDPI}, address = {Basel}, issn = {2072-666X}, doi = {10.3390/mi16030306}, pages = {1 -- 12}, abstract = {In a number of previous publications, scattering theory for N-pole semiconductor quantum devices was developed. In the framework of the Landauer-B{\"u}ttiker formalism, an S-matrix was constructed with the aid of an R-matrix providing a mapping of the in-going waves onto the out-going waves. These waves include propagating waves and evanescent waves, the latter of which decay exponentially in the leads which are connected to the active region of the N-pole device. In order to formulate the current conservation in the N-pole device, it is necessary to define the current S-matrix schematically as S˜=k1/2Sk-1/2, where k contains the information about the k-vectors of the mentioned in- and out-going waves. In this paper, we show how the complete current S-matrix is calculated including the coupling between the propagating and evanescent components and coupling to the bound states in the active device region. One then finds a sub-matrix of S˜which is unitary and which is restricted to the space of the propagating components. We demonstrate that current conservation is associated with the unitarity just of this sub-matrix.}, language = {en} }