2015/08/31 by Davide Pastorello
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Complex projective space #Controllability #Hamiltonian (control theory) #Hilbert space #Mathematics #Method of quantum characteristics #Noncommutative and Quantum Gravity Theories #POVM #Physics #Projective Hilbert space #Projective space #Projective test #Pure mathematics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum dynamics #Quantum mechanics #Quantum operation #Reproducing kernel Hilbert space #SIC-POVM #math-ph #math.MP
paper · pdf · doi:10.1016/s0034-4877(17)30020-4
published as Reports on Mathematical Physics Vol. 79, Issue 1, pp 53-66 (2017) · 11 pages
arxiv created 2016/05/03 · openalex publication_date 2017/02/01 · arxiv updated 2017/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A quantum theory in a finite-dimensional Hilbert space can be geometrically formulated as a proper Hamiltonian theory as explained in [2, 3, 7, 8]. From this point of view a quantum system can be described in a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by projective Hilbert space. This paper is devoted to investigate how the notion of accessibility algebra from classical control theory can be applied within geometric Hamiltonian formulation of Quanum Mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. Fubini-Study metric on projective space is also discussed.