For one monitored jump operator commuting with the Hamiltonian, quantum trajectories converge to an eigenstate of L†L in the long-time limit if and only if the squared jump amplitudes |l_i|² are all distinct.
(23) Here|ψ⟩ t denotes the pure conditional state given the measurement countmand measurement timet
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Conditions for implementing projective measurements through continuous monitoring
For one monitored jump operator commuting with the Hamiltonian, quantum trajectories converge to an eigenstate of L†L in the long-time limit if and only if the squared jump amplitudes |l_i|² are all distinct.