Entropic coherence of a battery, the relative entropy between its state and its energy-dephased version, must grow at least as the logarithm of the desired gate precision, making finite-dimensional batteries fundamentally imprecise.
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The entropic coherence is a necessary resource for non-energy preserving gates
Entropic coherence of a battery, the relative entropy between its state and its energy-dephased version, must grow at least as the logarithm of the desired gate precision, making finite-dimensional batteries fundamentally imprecise.