Dissipative "Groups" and the Bloch Ball

Allan I. Solomon; Cambridge); DAMTP; Open University; Sonia G. Schirmer (Quantum Processes Group

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arxiv quant-ph/0211027 v1 pith:3ECEKRE7 submitted 2002-11-06 quant-ph

Dissipative "Groups" and the Bloch Ball

Allan I. Solomon , Sonia G. Schirmer (Quantum Processes Group , Open University , DAMTP , Cambridge) This is my paper

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keywords blochballsemi-groupactionalgebracontrolcorrespondingdissipation

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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.

Dissipative "Groups" and the Bloch Ball

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