# New computable entanglement monotones from formal group theory

## TL;DR

This paper introduces a new family of computable entanglement measures derived from formal group theory, which generalize logarithmic negativity and are useful for studying entanglement in many-body quantum systems.

## Contribution

It develops a novel mathematical framework for entanglement monotones based on formal group theory, enabling algebraic and composable analysis of quantum entanglement.

## Key findings

- New family of entanglement measures generalizing logarithmic negativity
- Measures are algebraically composable and computable for tensor products
- Potential applications in studying separability, criticality, and conformal sectors of quantum states

## Abstract

We present a mathematical construction of new quantum information measures that generalize the notion of logarithmic negativity. Our approach is based on formal group theory. We shall prove that this family of generalized negativity functions, due their algebraic properties, is suitable for studying entanglement in many-body systems. Under mild hypotheses, the new measures are computable entanglement monotones. Also, they are composable: their evaluation over tensor products can be entirely computed in terms of the evaluations over each factor, by means of a specific group law. In principle, they might be useful to study separability and (in a future perspective) criticality of mixed states, complementing the role of R\'enyi's entanglement entropy in the discrimination of conformal sectors for pure states.