2015/12/31 by Fattah Sakuldee, Sujin Suwanna
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Dissipative system #Dynamical systems theory #Geometry #Hilbert space #Mathematical analysis #Mathematics #Molecular spectroscopy and chirality #Physics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Scaling #Spectroscopy and Quantum Chemical Studies #Statistical physics #cs.IT #math-ph #math.IT #math.MP #quant-ph
paper · pdf · doi:10.1016/j.physa.2018.04.097
openalex created_date 2016/06/24 · arxiv created 2018/04/28 · openalex publication_date 2018/05/03 · arxiv updated 2019/02/18 · openalex updated_date 2026/08/05
We investigate a decomposition of a unital Lindblad dynamical map of an open quantum system into two distinct types of mapping on the Hilbert-Schmidt space of quantum states. One component of the decomposed map corresponds to reversible behaviours, while the other to irreversible characteristics. For a finite dimensional system, we employ real vectors or Bloch representations and express a dynamical map on the state space as a real matrix acting on the representation. It is found that rotation and scaling transformations on the real vector space, obtained from the real-polar decomposition, form building blocks for the dynamical map. Consequently, the change of the linear entropy or purity, which indicates dissipative behaviours, depends only on the scaling part of the dynamical matrix. The rate of change of the entropy depends on the structure of the scaling part of the dynamical matrix, such as eigensubspace partitioning, and its relationship with the initial state. In particular, the linear entropy is expressed as a weighted sum of the exponential-decay functions in each scaling component, where the weight is equal to \vertxk(ρ)\vert2 of the initial state ρ in the subspace. The dissipative behaviours and the partition of eigensubspaces in the decomposition are discussed and illustrated for qubit systems.