New proof via Lyapunov exponents that the largest decay rate Γ_max in a d-dimensional quantum master equation satisfies Γ_max ≤ κ_d times the sum of the other d²-1 decay rates, with κ_d depending only on d and the map class.
Assessing non-Markovian dynamics
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abstract
We investigate what a snapshot of a quantum evolution - a quantum channel reflecting open system dynamics - reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of `Markovianity' is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations.
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quant-ph 1years
2025 1verdicts
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Universal bound on the Lyapunov spectrum of quantum master equations
New proof via Lyapunov exponents that the largest decay rate Γ_max in a d-dimensional quantum master equation satisfies Γ_max ≤ κ_d times the sum of the other d²-1 decay rates, with κ_d depending only on d and the map class.