Amplifying asymmetry with correlating catalysts

We investigate the fundamental constraint on amplifying the asymmetry in quantum states with correlating catalysts. Here a correlating catalyst is a finite-dimensional auxiliary, which exactly preserves its reduced state while allowed to become correlated with the quantum system. Interestingly, we prove that under translationally invariant operations, uncorrelating catalysts in pure states are useless in any state transformation, while with a correlating catalyst, one can extend 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 an 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.

Figure 1

Comparison of the TIO cone and the CCTIO cone with two-dimensional and three-dimensional catalysts of a qubit state. The initial state is $\rho \left(\eta \right)$ as in Eq. (3) with $\eta =0.3$.