  Non-Abelian anyons, a promising platform for fault-tolerant topological
quantum computation, adhere to the charge super-selection rule (cSSR), which
imposes restrictions on physically allowed states and operations. However, the
ramifications of cSSR and fusion rules in anyonic quantum information theory
remain largely unexplored. In this study, we unveil that the
information-theoretic characteristics of anyons diverge fundamentally from
those of non-anyonic systems such as qudits, bosons, and fermions and display
intricate structures. In bipartite anyonic systems, pure states may have
different marginal spectra, and mixed states may contain pure marginal states.
More striking is that in a pure entangled state, parties may lack equal access
to entanglement. This entanglement asymmetry is manifested in quantum
teleportation employing an entangled anyonic state shared between Alice and
Bob, where Alice can perfectly teleport unknown quantum information to Bob, but
Bob lacks this capability. These traits challenge conventional understanding,
necessitating new approaches to characterize quantum information and
correlations in anyons. We expect that these distinctive features will also be
present in non-Abelian lattice gauge field theories. Our findings significantly
advance the understanding of the information-theoretic aspects of anyons and
may lead to realizations of quantum communication and cryptographic protocols
where one party holds sway over the other.
