  Can a sender non-interactively transmit one of two strings to a receiver
without knowing which string was received? Does there exist
minimally-interactive secure multiparty computation that only makes (black-box)
use of symmetric-key primitives? We provide affirmative answers to these
questions in a model where parties have access to shared EPR pairs, thus
demonstrating the cryptographic power of this resource.
  First, we construct a one-shot (i.e., single message) string oblivious
transfer (OT) protocol with random receiver bit in the shared EPR pairs model,
assuming the (sub-exponential) hardness of LWE. Building on this, we show that
{\em secure teleportation through quantum channels} is possible. Specifically,
given the description of any quantum operation $Q$, a sender with (quantum)
input $\rho$ can send a single classical message that securely transmits
$Q(\rho)$ to a receiver. That is, we realize an ideal quantum channel that
takes input $\rho$ from the sender and provably delivers $Q(\rho)$ to the
receiver without revealing any other information. This immediately gives a
number of applications in the shared EPR pairs model: (1) non-interactive
secure computation of unidirectional \emph{classical} randomized
functionalities, (2) NIZK for QMA from standard (sub-exponential) hardness
assumptions, and (3) a non-interactive \emph{zero-knowledge} state synthesis
protocol.
  Next, we construct a two-round (round-optimal) secure multiparty computation
protocol for classical functionalities in the shared EPR pairs model that is
\emph{unconditionally-secure} in the (quantum-accessible) random oracle model.
