2021/08/27 by Khvedelidze, Arsen, Mladenov, Dimitar, Torosyan, Astghik · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2108.12499
Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an N-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N)-invariant counterpart of the N-level state space \mathfrakPN, i.e., the unitary orbit space \mathfrakPN/SU(N). It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of \mathfrakPN/SU(N). To illustrate the general situation, a detailed description of \mathfrakPN/SU(N) for low-level systems: qubit (N=2) , qutrit (N=3) , quatrit (N=4) - will be given.