Assembling Large Entangled States in the Rényi-Ingarden-Urbanik Entropy Measure under the SU(2)-Dynamics Decomposition for Systems Built from Two-Level Subsystems

Quantum Information is a discipline derived from Quantum Mechanics which uses quantum systems to exploit their states as information recipients. Normally, these states are conformed by two-level systems to reproduce the binary nature underlying the classical computation structure. Quantum evolution is then controlled to reproduce convenient information processing operations. Evolution could be hard to be controlled. SU(2) decomposition procedure lets to set a binary structure of processing when a convenient basis is selected to set the dynamics description. In this work, we exploit this procedure for a generic Hamiltonian in order to set the process to reduce arbitrary states into simplest ones. For this work, we use customary SU(2) operations on local and entangled states. These operations are described in the development. They involve 1, 2 and 4-local operations meaning the number of quantum parties involved, in agreement with the decomposition procedure scope. This task is complex in spite the difficulty to set a general way to manipulate the entanglement in the system. We are particularly interested on the application of stochastic procedures based in SU(2) decomposition operations to achieve that goal. In order to have a measure of the advancement of the last task, we use the RényiIngarden-Urbanik entropy to describe the whole spectrum of entanglement in the large systems through the assembling/disassembling of the state.