Dissipative "Groups" and the Bloch Ball

Solomon, Allan I. and Schirmer, Sonia G. (2002). Dissipative "Groups" and the Bloch Ball. In: Proceedings of Group 24, Physical and Mathematical Aspects of Symmetry, Institute of Physics Conference Series, Jul 2002, Paris, France.

URL: http://xxx.soton.ac.uk/abs/quant-ph/0211027


We show that a quantum control procedure on a two-level system including dissipation gives rise to a semi-group corresponding to the Lie algebra semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in the Bloch ball.

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