For Lindblad dynamics with local dissipation, a quantum i.i.d. product state is a steady state iff simple single-site and two-site conditions hold, and a broad class of systems has such product steady states.
Any Quantum Many-Body State under Local Dissipation will be Disentangled in Finite Time
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abstract
We prove that any quantum many-spin state under genetic local dissipation will be fully separable after a finite time independent of the system size. Such a sudden death of many-body entanglement occurs universally provided that there is a finite damping gap and the unique steady-state density matrix is of full rank. This result is rigorously derived by combining a state-reconstruction identity based on random measurements and the convergence bound for quantum channels. Related works and possible generalizations are also discussed.
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Quantum i.i.d. Steady States in Open Many-Body Systems
For Lindblad dynamics with local dissipation, a quantum i.i.d. product state is a steady state iff simple single-site and two-site conditions hold, and a broad class of systems has such product steady states.