super-classical precision [44], 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.
5 Conclusion
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.
Acknowledgements
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-
den Markov Models.’
References
[1] T. F. Rønnow, Z. Wang, J. Job, S. Boixo, S. V.
Isakov, D. Wecker, J. M. Martinis, D. A. Lidar,
and M. Troyer, Science 345, 420 (2014).
[2] E. T. Campbell, B. M. Terhal, and C. Vuillot,
Nature 549, 172 (2017).
[3] J. Preskill, Quantum 2, 79 (2018).
[4] N. Gisin and R. Thew, Nature Photonics 1, 165
(2007).
[5] A. Galindo and M. A. Martín-Delgado, Rev. Mod.
Phys. 74, 347 (2002).
[6] I. M. Georgescu, S. Ashhab, and F. Nori, Rev.
Mod. Phys. 86, 153 (2014).
[7] V. Giovannetti, S. Lloyd, and L. Maccone, Na-
ture Photonics 5, 222 (2011).
[8] G. Tóth and I. Apellaniz, J. Phys. A: Math. and
Theor. 47, 424006 (2014).
[9] C. L. Degen, F. Reinhard, and P. Cappellaro,
Rev. Mod. Phys. 89, 035002 (2017).
[10] J. Åberg, “Quantifying superposition,” (2006),
arXiv:quant-ph/0612146 [quant-ph] .
[11] T. Baumgratz, M. Cramer, and M. B. Plenio,
Phys. Rev. Lett. 113, 140401 (2014).
[12] A. Streltsov, G. Adesso, and M. B. Plenio, Rev.
Mod. Phys. 89, 041003 (2017).
[13] A. Winter and D. Yang, Phys. Rev. Lett. 116,
120404 (2016).
[14] D. Egloff, J. M. Matera, T. Theurer, and M. B.
Plenio, Phys. Rev. X 8, 031005 (2018).
[15] K. Ben Dana, M. García Díaz, M. Mejatty, and
A. Winter, Phys. Rev. A 95, 062327 (2017).
[16] M. García Díaz, K. Fang, X. Wang, M. Rosati,
M. Skotiniotis, J. Calsamiglia, and A. Winter,
Quantum 2, 100 (2018).
[17] T. Theurer, D. Egloff, L. Zhang, and M. B. Ple-
nio, Phys. Rev. Lett. 122, 190405 (2019).
[18] Y. Liu and X. Yuan, Phys. Rev. Research 2,
012035 (2020).
[19] G. Gour and A. Winter, Phys. Rev. Lett. 123,
150401 (2019).
[20] A. Smirne, D. Egloff, M. García Díaz, M. B. Ple-
nio, and S. F. Huelga, Quantum Science and
Technology 4, 01LT01 (2018).
[21] H. P. Breuer and F. Petruccione, The Theory of
Open Quantum Systems (Oxford University Press,
2002).
[22] V. Gorini, A. Kossakowski, and E. C. G. Sudar-
shan, Journal of Mathematical Physics 17, 821
(1976).
[23] G. Lindblad, Communications in Mathematical
Physics 48, 119 (1976).
[24] B.-G. Englert and G. Morigi, “Coherent evolution
in noisy environments,” (Springer-Verlag, 2002)
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