Dissipative "Groups" and the Bloch Ball
Allan I. Solomon, Sonia G. Schirmer (Quantum Processes Group, Open, University, DAMTP, Cambridge)
TL;DR
This paper explores how dissipation in quantum control of a two-level system leads to a semi-group structure acting on the Bloch ball, revealing new mathematical insights into quantum dynamics with dissipation.
Contribution
It introduces a semi-group model based on the Lie algebra semi-direct sum gl(3,R)+R^3 for dissipative quantum control on a two-level system.
Findings
Dissipative quantum control induces a semi-group structure.
The evolution can be represented as an action on the Bloch ball.
The semi-group corresponds to a specific Lie algebra semi-direct sum.
Abstract
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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Taxonomy
TopicsQuantum chaos and dynamical systems · Quantum optics and atomic interactions · Nonlinear Photonic Systems