Composite Quantum Systems

Elemér Elad Rosinger

A family of {\it quantumness spaces} is identified and precisely defined. They are spaces which characterize the difference between states given by classical compositions of systems, and on the other hand, states corresponding to their quantum compositions. Consequently, the quantum composition of systems is {\it reduced} to two classical compositions. A family of rankings is also defined for the respective family of quantumness.

Додин Дмитрий Валерьевич, I. G. Kovalenko, Alexander I. Lvovsky

A composite quantum system is a fundamental object in quantum informatics. A composite quantum system is considered a system whose dimension is a composite integer number whereas the prime integers may only correspond to non‐composite systems. Entanglement and the procedure of reduction to a subsystem via averaging over environment are only formulated for composite systems. In the present report we introduce a procedure of decomposition into ‘subsystems’ for a system whose dimension is an arbitrary number including a prime integer. This procedure generalizes the standard procedure of reduction. In the particular case of a non‐composite system the space of states of the decomposed system splits into direct sum of subspaces of states and the average dimension of subspaces is a fractional number. We compare the properties of the introduced procedure of decomposition and the standard separation into subsystems.

Federico Holik

Sheng-Wen Li, Da Xu, Xulin Liu +1 more

We study the thermalization of a composite quantum system consisting of several subsystems, where only a small one of the subsystem contacts with a heat bath in equilibrium, while the rest of the composite system is contact free. We show that the whole composite system still can be thermalized after a relaxation time long enough, if the energy level structure of the composite system is connected, which means any two energy levels of the composite system can be connected by direct or indirect quantum transitions. With an example where an multi-level system interacts with a set of harmonic oscillators via non-demolition coupling, we find that the speed of relaxation to the global thermal state is suppressed by the multi-Franck-Condon factor due to the displacements of the Fock states when the degrees of freedom is large.

V. M. Akulin