# Coherence quantifiers from the viewpoint of their decreases in the measurement process

## TL;DR

This paper introduces new coherence quantifiers based on the L"uders measurement picture, analyzing quantum coherence loss during measurements and exemplifying with state discrimination scenarios.

## Contribution

It develops coherence quantifiers aligned with the L"uders measurement framework, expanding the characterization of quantum coherence loss during generalized measurements.

## Key findings

- Coherence quantifiers satisfy properties similar to basis-dependent measures.
- Losses of quantum coherence are characterized during generalized measurements.
- Application to unambiguous state discrimination illustrates extreme coherence loss scenarios.

## Abstract

Measurements can be considered as a genuine example of processes that crush quantum coherence. In the case of an observable with degeneracy, the formulations of L\"{u}ders and von Neumann are known. These pictures postulate the two different states of a system immediately following the act of measurement. Hence, they are associated with divers variants of coherence losses during the measurement. Recent studies have focused on several ways to characterize quantum coherence appropriately. One of the existing types of quantifier is based on quantum $\alpha$-divergences of the Tsallis type. In this paper, we introduce coherence quantifiers associated with the L\"{u}ders picture of quantum measurements. The are shown to satisfy the same properties as coherence $\alpha$-quantifiers related to some orthonormal basis. Further, we consider losses of quantum coherence during a generalized measurement. The proposed approach is exemplified with unambiguous state discrimination; extreme properties of the states to be discriminated are clearly shown.