# Reference frames which separately store non-commuting conserved quantities

## TL;DR

This paper investigates how non-commuting conserved quantities like angular momentum components can be stored separately in different parts of a reference frame, impacting quantum thermodynamics and resource theories.

## Contribution

It demonstrates that non-commuting conserved quantities can be independently stored in different reference frame components, extending understanding of quantum conservation laws.

## Key findings

- Components of angular momentum can be stored separately in reference frames.
- The results extend to other non-commuting conserved quantities.
- Implications for quantum thermodynamics of non-commuting observables.

## Abstract

Even in the presence of conservation laws, one can perform arbitrary transformations on a system if given access to a suitable reference frame, since conserved quantities may be exchanged between the system and the frame. Here we explore whether these quantities can be separated into different parts of the reference frame, with each part acting as a `battery' for a distinct quantity. For systems composed of spin-$\frac12$ particles, we show that the components of angular momentum $S_x$, $S_y$ and $S_z$ (non-commuting conserved quantities) may be separated in this way, and also provide several extensions of this result. These results also play a key role in the quantum thermodynamics of non-commuting conserved quantities.