# General measure for macroscopic quantum states beyond "dead and alive"

## TL;DR

This paper introduces a new measure based on mutual information to characterize complex macroscopic quantum superpositions, extending beyond traditional 'dead and alive' states, and explores its implications for quantum state robustness.

## Contribution

It proposes a novel, broadly applicable measure for macroscopic quantum states that encompasses superpositions with multiple components and mixed states, bridging existing gaps in quantification methods.

## Key findings

- The measure effectively distinguishes complex superpositions.
- Connections established with quantum discord and other measures.
- The measure relates quantum size to noise vulnerability.

## Abstract

We consider the characterization of quantum superposition states beyond the pattern "dead and alive". We propose a measure that is applicable to superpositions of multiple macroscopically distinct states, superpositions with different weights as well as mixed states. The measure is based on the mutual information to characterize the distinguishability between multiple superposition states. This allows us to overcome limitations of previous proposals, and to bridge the gap between general measures for macroscopic quantumness and measures for Schr\"odinger-cat type superpositions. We discuss a number of relevant examples, provide an alternative definition using basis-dependent quantum discord and reveal connections to other proposals in the literature. Finally, we also show the connection between the size of quantum states as quantified by our measure and their vulnerability to noise.