Abstract
A new condition for dynamical maps with time independent invariant state displaying Heisenberg divisibility is provided. This condition is trivially satisfied for a Markovian semigroup. However, beyond Markovian semigroups it provides a nontrivial characteristics of quantum Markovianity. Interestingly, when the invariant state is pure one recovers a condition based on Wigner–Yanase skew information.
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