= Thomas Barthel
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<Thomas Barthel> and <Yikang Zhang> established algebraic tests for <Davies irreducibility> of Markovian open-system quantum evolution. Their criterion connects the <Lindblad operators> and effective drift operator with the algebra they generate.<Criteria for Davies Irreducibility of Markovian Quantum Dynamics by Yikang Zhang and Thomas Barthel>[Abstract and main algebraic irreducibility criterion]{ref}
For a finite-dimensional irreducible system, the stationary <density matrix> is unique and full rank. The work distinguishes different notions of reducibility, preventing a convenient algebraic test from being applied to the wrong dynamical definition.
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