For fixed quantum batteries, random unitary, CPTP, and general quantum maps extract the same average energy, but fluctuations vanish only in a Cesàro limit over auxiliary dimensions; finite-ancilla scalings are 1/n (CPTP) and ln(n)/n (general maps).
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Fluctuation in energy extraction from quantum batteries: How open should the system be to control it?
For fixed quantum batteries, random unitary, CPTP, and general quantum maps extract the same average energy, but fluctuations vanish only in a Cesàro limit over auxiliary dimensions; finite-ancilla scalings are 1/n (CPTP) and ln(n)/n (general maps).