# Properties of Quantum Reactivity for a Multipartite State

## TL;DR

This paper introduces quantum reactivity, a geometric measure for quantum correlations in multipartite states, generalizing previous two-qubit concepts and demonstrating key properties like invariance and monotonicity.

## Contribution

It proposes a novel information geometry-based measure called quantum reactivity for multipartite states, extending previous two-qubit measures and establishing its key properties.

## Key findings

- Reactivity is invariant under local unitaries.
- Reactivity is non-increasing under local operations and classical communication.
- Reactivity cannot be maximized by classical correlations.

## Abstract

We discuss the properties of quantum state reactivity as a measure for quantum correlation. This information geometry-based definition is a generalization of the two qubit construction of Schumacher to multipartite quantum states. It requires a generalization of information distance to information areas as well as to higher-dimensional volumes. The reactivity is defined in the usual chemistry way as a ratio of surface area to volume. The reactivity is an average over all detector settings. We show that this measure posses the key features required for a measure of quantum correlation. We show that it is invariant under local unitary transformations, non-increasing under local operations and classical communication, and monotonic. Its maximum bound can't be obtained using only classical correlation. Furthermore, reactivity is an analytic function of measurement probabilities and easily extendable to higher multipartite states.