Schrödinger and Heisenberg non-Markovianity are inequivalent, with some quantum tasks requiring memory in both pictures and others in only one, plus necessary conditions detectable from one picture.
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For the Fano-Anderson model with Lorentzian spectral density, the TCL expansion converges within a radius set by the detuning-to-width ratio, and its second and fourth orders represent non-Markovianity differently as measured by Bures distance evolution.
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Schr\"odinger and Heisenberg non-Markovianity in quantum information tasks
Schrödinger and Heisenberg non-Markovianity are inequivalent, with some quantum tasks requiring memory in both pictures and others in only one, plus necessary conditions detectable from one picture.
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Expansion of time-convolutionless non-Markovian quantum master equations: A case study using the Fano-Anderson model
For the Fano-Anderson model with Lorentzian spectral density, the TCL expansion converges within a radius set by the detuning-to-width ratio, and its second and fourth orders represent non-Markovianity differently as measured by Bures distance evolution.