A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper geometric Hamiltonian theory as explained in [2, 3, 7, 9]. From this point of view a quantum system can be described within a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by a projective Hilbert space. This paper is devoted to investigating how the notion of an accessibility algebra from classical control theory can be applied within the geometric Hamiltonian formulation of quantum mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. the Fubini–Study metric on projective space is also discussed.

Pastorello D. (2017). A geometric approach to quantum control in projective Hilbert spaces. REPORTS ON MATHEMATICAL PHYSICS, 79(1), 53-66 [10.1016/S0034-4877(17)30020-4].

A geometric approach to quantum control in projective Hilbert spaces

Pastorello D.
2017

Abstract

A quantum theory in a finite-dimensional Hilbert space can be formulated as a proper geometric Hamiltonian theory as explained in [2, 3, 7, 9]. From this point of view a quantum system can be described within a classical-like framework where quantum dynamics is represented by a Hamiltonian flow in the phase space given by a projective Hilbert space. This paper is devoted to investigating how the notion of an accessibility algebra from classical control theory can be applied within the geometric Hamiltonian formulation of quantum mechanics to study controllability of a quantum system. A new characterization of quantum controllability in terms of Killing vector fields w.r.t. the Fubini–Study metric on projective space is also discussed.
2017
Pastorello D. (2017). A geometric approach to quantum control in projective Hilbert spaces. REPORTS ON MATHEMATICAL PHYSICS, 79(1), 53-66 [10.1016/S0034-4877(17)30020-4].
Pastorello D.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/926009
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