  Nonlocality and its connections to entanglement are fundamental features of
quantum mechanics that have found numerous applications in quantum information
science. A set of correlations is said to be nonlocal if it cannot be
reproduced by spacelike-separated parties sharing randomness and performing
local operations. An important practical consideration is that the runtime of
the parties has to be shorter than the time it takes light to travel between
them. One way to model this restriction is to assume that the parties are
computationally bounded. We therefore initiate the study of nonlocality under
computational assumptions and derive the following results:
  (a) We define the set $\mathsf{NeL}$ (not-efficiently-local) as consisting of
all bipartite states whose correlations arising from local measurements cannot
be reproduced with shared randomness and \emph{polynomial-time} local
operations.
  (b) Under the assumption that the Learning With Errors problem cannot be
solved in \emph{quantum} polynomial-time, we show that
$\mathsf{NeL}=\mathsf{ENT}$, where $\mathsf{ENT}$ is the set of \emph{all}
bipartite entangled states (pure and mixed). This is in contrast to the
standard notion of nonlocality where it is known that some entangled states,
e.g. Werner states, are local. In essence, we show that there exist (efficient)
local measurements producing correlations that cannot be reproduced through
shared randomness and quantum polynomial-time computation.
  (c) We prove that if $\mathsf{NeL}=\mathsf{ENT}$ unconditionally, then
$\mathsf{BQP}\neq\mathsf{PP}$. In other words, the ability to certify all
bipartite entangled states against computationally bounded adversaries gives a
non-trivial separation of complexity classes.
  (d) Using (c), we show that a certain natural class of 1-round delegated
quantum computation protocols that are sound against $\mathsf{PP}$ provers
cannot exist.
