Controllability properties for finite dimensional quantum Markovian master equations

2002/11/28 by Claudio Altafini, C. Altafini · 8 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Spectroscopy and Quantum Chemical Studies #quant-ph

paper · pdf · doi:10.1063/1.1571221

published as J. Math. Phys., 44(6):2357-2372, 2003 · 15 pages

arxiv created 2002/11/28 · openalex publication_date 2003/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.

Citations

• Using unitary operations to preserve quantum states in the presence of relaxation
• Completely positive dynamical semigroups of N-level systems
• Universal simulation of Markovian quantum dynamics

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• Indirect control with a quantum accessor: Coherent control of multilevel system via a qubit chain