1Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
2Institute of Theoretical Physics and IQST, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany
3Institute of Theoretical Physics, Technical University Dresden, D-01062 Dresden, Germany
4Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, via Celoria 16, 20133 Milan, Italy
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Abstract
Quantum coherence generated in a physical process can only be cast as a potentially useful resource if its effects can be detected at a later time. Recently, the notion of non-coherence-generating-and-detecting (NCGD) dynamics has been introduced and related to the classicality of the statistics associated with sequential measurements at different times. However, in order for a dynamics to be NCGD, its propagators need to satisfy a given set of conditions for $all$ triples of consecutive times. We reduce this to a finite set of $d(d-1)$ conditions, where $d$ is the dimension of the quantum system, provided that the generator is time-independent. Further conditions are derived for the more general time-dependent case. The application of this result to the case of a qubit dynamics allows us to elucidate which kind of noise gives rise to non-coherence-generation-and-detection.
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