super-classical precision , which can be even raised
to the ultimate Heisenberg limit by means of error cor-
rection [50–52]. This provides us with an example of
how the capability to generate coherences (in the rele-
vant basis) and later convert them to populations has to
be understood as a prerequisite to perform tasks which
rely on the advantage given by the use of quantum fea-
tures. However, CGD in itself does not guarantee that
such an advantage over any possible classical counter-
part is actually achieved.
In this work we have shown that fulﬁlling a ﬁnite num-
ber of criteria is necessary and suﬃcient to ensure that
a given quantum dynamics with time-independent gen-
erator cannot generate and subsequently detect coher-
ence. Importantly, these conditions are given in terms
of the generator of the dynamics itself, which makes
them even more convenient when one wants to char-
acterize the evolution of a certain open system. In the
more general case of a time-dependent generator, an un-
countably inﬁnite number of conditions arises. We have
exempliﬁed our results for the case of a GKSL qubit
dynamics, providing the deﬁning properties of genera-
tors that give rise to coherence non-generating as well
as coherence non-activating maps, and applied our ﬁnd-
ings to analyze the coherence-generating-and-detecting
capabilities of the open-system dynamics describing a
typical Ramsey protocol.
Our method provides a way of assessing the intercon-
version between coherence and population which repre-
sents a prerequisite for the potential use of coherence as
a resource in quantum information technology.
The authors thank Andreu Riera and Philipp Stras-
berg for interesting discussions on various aspects of
the present work. The authors acknowledge support
from Spanish MINECO, project FIS2016-80681-P with
the support of AEI/FEDER funds; the Generalitat de
Catalunya, project CIRIT 2017-SGR-1127; the ERC
Synergy Grant BioQ. MGD is supported by a doc-
toral studies fellowship of the Fundación “la Caixa,”
grant LCF/BQ/DE16/11570017. MS is supported by
the Spanish MINECO, project IJCI-2015-24643. MR
acknowledges partial ﬁnancial support by the Baidu-
UAB collaborative project ‘Learning of Quantum Hid-
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