  Quantum teleportation is the process of transferring quantum information
using classical communication and pre-shared entanglement. This process can
benefit from the use of catalysts, which are ancillary entangled states that
can enhance teleportation without being consumed. While chemical catalysts
undergoing deactivation invariably exhibit inferior performance compared to
those unaffected by deactivation, quantum catalysts, termed embezzling
catalysts, that are subject to deactivation, may surprisingly outperform their
non-deactivating counterparts. In this work, we present teleportation protocols
with embezzling catalyst that can achieve arbitrarily high fidelity, namely the
teleported state can be made arbitrarily close to the original state, with
finite-dimensional embezzling catalysts. We show that some embezzling catalysts
are universal, meaning that they can improve the teleportation fidelity for any
pre-shared entanglement. We also explore methods to reduce the dimension of
catalysts without increasing catalyst consumption, an essential step towards
realizing quantum catalysis in practice.
