Accessible coherence in open quantum system dynamics

María García Díaz1, Benjamin Desef2, Matteo Rosati1, Dario Egloff2,3, John Calsamiglia1, Andrea Smirne2,4, Michaelis Skotiniotis1, and Susana F. Huelga2

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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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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[5] A Smirne, T Nitsche, D Egloff, S Barkhofen, S De, I Dhand, C Silberhorn, S F Huelga, and M B Plenio, "Experimental control of the degree of non-classicality via quantum coherence", Quantum Science and Technology 5 4, 04LT01 (2020).

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[7] Masaya Takahashi, Swapan Rana, and Alexander Streltsov, "Creating and destroying coherence with quantum channels", Physical Review A 105 6, L060401 (2022).

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