Phase-preserving steady-state operations beyond Lindblad

Abstract:We consider a class of non-unitary operations that is naturally implemented via a combination of projective measurement and unitary operators. We implement these operations without using measurements by coupling the system to an infinite set of ancilla states and time-evolving with a single time-independent Hamiltonian. The infinite ancilla enables the main system to reach a local steady state that preserves initial phase information. We prove that these steady state operations are not describable as a mapping from initial to steady state of a time-independent Lindblad equation. As an additional degree of control, we show that the spectral resonance between the system and the ancilla acts as a switch that turns the operation on and off, and we derive a closed-form expression that quantifies the sharpness of this switch. We further find numerically that the phase preservation survives moderate disorder, over a time window set by the size of the ancilla. This Hamiltonian framework therefore provides a route to autonomous quantum control beyond what standard time-independent dissipative engineering can achieve.

arXiv:2510.10394 [quant-ph]

(or arXiv:2510.10394v3 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.10394 Focus to learn more arXiv-issued DOI via DataCite

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