  Quantum teleportation is a phenomenon arising from entanglement, decisively
distinguishing the classical and quantum worlds. The recent success of
many-body quantum teleportation is even more surprising: although input
information is initially dispersed and encoded into the many-body state in a
complex way, the teleportation process can refocus this highly non-local
information at the receiver's end. This success manifests intriguing capability
of many-body systems in quantum information processing. Current studies
indicate that information scrambling, a generic dynamic process in many-body
systems, underlies the effectiveness of many-body quantum teleportation.
However, this process is known to undergo a novel scrambling-dissipation
transition in the presence of environments. How environments affect the quantum
information processing capability of many-body systems calls for further
investigation. In this work, we study many-body quantum teleportation in the
presence of environments. We predict two emergent critical points that hallmark
the transitions of the teleportation performance from the quantum regime to the
classical regime, and finally to the no-signal regime as the system-environment
coupling, quantified by $\gamma$, increases. In the quantum regime,
teleportation can outperform its classical counterparts, while in the classical
regime, it can be replaced by a classical channel. Our prediction is based on a
generic argument harnessing the relationship between many-body quantum
teleportation and information scrambling, corroborated by solvable Brownian
Sachdev-Ye-Kitaev models.
