# Coherence and asymmetry cannot be broadcast

## TL;DR

This paper proves fundamental no-go theorems showing that quantum coherence related to conserved quantities cannot be broadcast or shared in finite-dimensional systems, revealing limits on manipulating quantum asymmetry.

## Contribution

It establishes that broadcasting quantum coherence is impossible in finite dimensions and clarifies conditions for catalytic coherence in infinite dimensions, addressing open questions in quantum information.

## Key findings

- Broadcasting of coherence is forbidden in finite-dimensional systems.
- Catalytic coherence requires infinite-dimensional reference systems.
- The results impose fundamental limits on quantum resource distribution.

## Abstract

In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing that this is forbidden by quantum mechanics in every finite-dimensional system. In doing so we also answer some open questions in the quantum information literature concerning the sharing of timing information of a clock and the possibility of catalysis in quantum thermodynamics. We also prove that even weaker forms of broadcasting, of which Aberg's `catalytic coherence' is a particular example, can only occur in the presence of infinite-dimensional reference systems. Our results set fundamental limits to the creation and manipulation of quantum coherence and shed light on the possibilities and limitations of quantum reference frames to act catalytically without being degraded.