Algebraic approaches for quantum information
C*-modules and quantum entanglement
Description of bipartite quantum systems by using C*-modules, non-commutative eigenvalue equations and Hamiltonian of the system dressed by its environment, weak adiabatic transport and dynamics of quantum entanglement, operator valued geometric phases. Control of bipartite quantum systems.
Quaternionic numbers and quantum decoherence
Competition between decoherence and quantum purification protocols: representations as chaotic dynamical systems on the quaternionic space, fractals involved by the decoherence-purification competition.
Categorical geometry of the dynamics of open quantum systems
Higher gauge theories and categorical bundles in dynamics of entangled systems or in contact with an environment, categories describing mixed states and their transformations.
- D. Viennot & J. Lages, A new kind of geometric phases in open quantum systems and higher gauge theory, J. Phys. A : Math. Theor. 44, 365301 (2011).
- D.Viennot & J. Lages, C*-geometric phase for mixed states: entanglement, decoherence and spin system, J. Phys. A: Math. Theor. 45, 365305 (2012).
- D. Viennot, Adiabatic quantum control hampered by entanglement, J. Phys. A: Math. Theor. 47, 295301 (2014).
- D. Viennot & L. Aubourg, Adiabatic theorem for bipartite quantum systems in weak coupling limit, J. Phys. A: Math. Theor. 48, 025301 (2015).
- D. Viennot, Non-abelian higher gauge theory and categorical bundle, Journal of Geometry and Physics 110, 407 (2016).
- D. Viennot, Purification of Lindblad dynamics, geometry of mixed states and geometric phases, J. Geom. Phys. 133, 42 (2018).
- D. Viennot, Competition between decoherence and purification: quaternionic representation and quaternionic fractals, Chaos, Solitons and Fractals 161, 112346 (2022)
