Characterization of a quasi-static environment with a qubit. (arXiv:1903.06463v1 [quant-ph])

We consider a qubit initalized in a superposition of its pointer states,
exposed to pure dephasing due to coupling to a quasi-static environment, and
subjected to a sequence of single-shot measurements projecting it on chosen
superpositions. We show how with a few of such measurements one can
significantly diminish one's ignorance about the environmental state, and how
this leads to increase of coherence of the qubit interacting with a properly
post-selected environmental state. We give theoretical results for the case of
a quasi-static environment that is a source of an effective field of Gaussian
statistics acting on a qubit, and for a nitrogen-vacancy center qubit coupled
to a nuclear spin bath, for which the Gaussian model applies qualitatively
provided one excludes from the environment nuclei that are strongly coupled to
the qubit. We discuss the reason for which the most probable sequences of
measurement results are the ones consisting of identical outcomes, and in this
way we shed light on recent experiment (D. D. Bhaktavatsala Rao et al.,
arXiv:1804.07111) on nitrogen-vacancy centers.

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