Geometrical analysis and entanglement measure of symmetric multiqubit states

We geometrically examine the entanglement in symmetric multiquibt states using the spin coherent states properties. We employ the Majorana representation to examine how coherent (polarized) and unpolarized states can be represented in the Bloch sphere and subsequently to quantify entanglement in multipartite systems. Entanglement can be viewed as a distance separate two points in Bloch sphere and how this notion can be extended for multipartite states in W class. This provides us with an entanglement measure for [Formula: see text]-states analogue to the notion of Concurrence.

Dynamics of Majorana-based qubits operated with an array of tunable gates

We study the dynamics of Majorana zero modes that are shuttled via local tuning of the electrochemical potential in a superconducting wire. By performing time-dependent simulations of microscopic lattice models, we show that diabatic corrections associated with the moving Majorana modes are quantitatively captured by a simple Landau-Zener description. We further simulate a Rabi-oscillation protocol in a specific qubit design with four Majorana zero modes in a single wire and quantify constraints on the timescales for performing qubit operations in this setup. Our simulations utilize a Majorana representation of the system, which greatly simplifies simulations of superconductors at the mean-field level.

Majorana algebras generated by a 2 ⁢ A {2A} algebra and one further axis

We consider Majorana algebras generated by three Majorana axes {a_{0}} , {a_{1}} and {a_{2}} such that {a_{0}} and {a_{1}} generate a dihedral algebra of type {2A} . We show that such an algebra must occur as a Majorana representation of one of 27 groups. These 27 groups coincide with the subgroups of the Monster that are generated by three {2A} -involutions a, b and c such that ab is also a {2A} -involution, which were classified by S. P. Norton in 1985. Our work relies on that of S. Decelle and consists of showing that certain groups do not admit Majorana representations.