Minimal number of observables for quantum tomography of systems with evolution given by double commutators

Abstract

In this paper, we analyze selected evolution models of N -level open quantum systems to find the minimal number of observables (Hermitian operators) such that their expectation values at some time instants determine the accurate representation of the quantum system. The assumption that lies at the foundation of this approach to quantum tomography claims that time evolution of an open quantum system can be expressed by the KossakowskiLindblad equation of the formρ = Lρ, which is the most general type of Markovian and time-homogeneous master equation which preserves trace and positivity. We consider the cases when the generator of evolution can be presented by means of two or more double commutators. Determining the minimal number of observables required for quantum tomography can be the first step towards optimal tomography models for N -level quantum systems.

Dynamic State Reconstruction of Quantum Systems Subject to Pure Decoherence

“…This approach aims to reconstruct the initial density matrix by the lowest possible number of distinct observables due to the utilization of the knowledge about the evolution of a quantum system (encoded, for example, in a GKSL equation [11,12]). For a given linear generator of evolution, one can compute the index of cyclicity, which expresses the minimal number of distinct observables required for quantum tomography [13][14][15]. The mean value of each observable is measured at several time instants over different copies of the system (prepared in the same unknown initial state).…”