Amplifying asymmetry with correlated catalysts

TL;DR

This paper explores how correlated catalysts can enhance asymmetry in quantum states, revealing that mixed-state catalysts can significantly expand the set of achievable state transformations under certain operations.

Contribution

It demonstrates that correlated catalysts in mixed states enable transformations impossible with pure catalysts, linking coherence restrictions to thermodynamics and quantum timing.

Findings

Pure state catalysts are ineffective under translationally invariant operations.

Mixed state catalysts can enlarge the set of accessible states.

Catalyst power increases with its dimension, enabling arbitrary state conversions.

Abstract

We investigate the basic constraint on amplifying the asymmetry in quantum states with correlated catalysts. Here a correlated catalyst is a finite-dimensional auxiliary, which exactly preserves its reduced state while allowed to become correlated to the quantum system. Interestingly, we prove that under translationally invariant operations, catalysts in pure states are useless in any state transformation, while with a correlated catalyst in a mixed state, one can enlarge the set of accessible states from an initially asymmetric state. Moreover, we show that the power of a catalyst increases with its dimension, and further, with a large enough catalyst, a qubit state with arbitrarily small amount of asymmetry can be converted to any mixed qubit state. In doing so, we build a bridge between two important results concerning the restrictions on coherence conversion, the no-broadcasting theorem and the catalytic coherence. Our results may also apply to the constraints on coherence evolution in quantum thermodynamics, and to the distribution of timing information between quantum clocks.