# Characterization of a quasi-static environment with a qubit

## TL;DR

This paper investigates how sequential measurements on a qubit can reduce environmental ignorance and enhance coherence, with theoretical models and experimental relevance to nitrogen-vacancy centers in quantum systems.

## Contribution

It introduces a method to decrease environmental uncertainty and increase qubit coherence through measurement sequences, supported by theoretical analysis and experimental insights.

## Key findings

- Sequential measurements reduce environmental ignorance.
- Post-selection increases qubit coherence.
- Most probable measurement sequences are identical outcomes.

## Abstract

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.