  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.
