Determining stationary-state quantum properties directly from system-environment interactions

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Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between the Lyapunov equation for dynamical systems and the steady-state solutions of a time-independent Lindblad master equation for bosonic modes. Exploiting bona-fide relations that characterize some genuine quantum properties (entanglement, classicality, and steerability), we obtain conditions on the dynamical parameters for which the system is driven to a steady-state possessing such properties. We also develop a method to capture the symmetries of a steady state based on symmetries of the Lyapunov equation. All the results and examples can be useful for steady-state engineering process.
Original languageEnglish
Article number052129
Number of pages12
JournalPhysical Review A (Atomic, Molecular, and Optical Physics)
Issue number5
Publication statusPublished - 28 Nov 2016


  • quant-ph


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