  We show that any language in nondeterministic time $\exp(\exp(\cdots
\exp(n)))$, where the number of iterated exponentials is an arbitrary function
$R(n)$, can be decided by a multiprover interactive proof system with a
classical polynomial-time verifier and a constant number of quantum entangled
provers, with completeness $1$ and soundness $1 - \exp(-C\exp(\cdots\exp(n)))$,
where the number of iterated exponentials is $R(n)-1$ and $C>0$ is a universal
constant. The result was previously known for $R=1$ and $R=2$; we obtain it for
any time-constructible function $R$.
  The result is based on a compression technique for interactive proof systems
with entangled provers that significantly simplifies and strengthens a protocol
compression result of Ji (STOC'17). As a separate consequence of this technique
we obtain a different proof of Slofstra's recent result (unpublished) on the
uncomputability of the entangled value of multiprover games.
  Finally, we show that even minor improvements to our compression result would
yield remarkable consequences in computational complexity theory and the
foundations of quantum mechanics: first, it would imply that the class MIP*
contains all computable languages; second, it would provide a negative
resolution to a multipartite version of Tsirelson's problem on the relation
between the commuting operator and tensor product models for quantum
correlations.

Quantum Physics;Computational Complexity