# Quantum Coherence, Coherent Information and Information Gain in Quantum Measurement

## TL;DR

This paper explores how quantum coherence limits information gain in quantum measurements, establishing bounds based on initial coherence, entropy exchange, and entanglement, with implications for optimizing measurement strategies.

## Contribution

It links quantum coherence to information gain in measurement, providing bounds and conditions for maximizing information transfer in quantum systems.

## Key findings

- Maximum information gain is bounded by initial coherence of the system.
- Information gain is limited by entropy exchange with the environment.
- Robustness of the apparatus enhances information gain.

## Abstract

A measurement is deemed successful, if one can maximize the information gain by the measurement apparatus. Here, we ask if quantum coherence of the system imposes a limitation on the information gain during quantum measurement. First, we argue that the information gain in a quantum measurement is nothing but the coherent information or the distinct quantum information that one can send from the system to apparatus. We prove that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system. Further, we illustrate the measurement scenario in the presence of environment. We argue that the information gain is upper bounded by the entropy exchange between the system and the apparatus. Also, to maximize the information gain, both the initial coherence of the apparatus, and the final entanglement between the system and apparatus should be maximum. Moreover, we find that for a fixed amount of coherence in the final apparatus state the more robust apparatus is, the more will be the information gain.