
Quantum proof systems for iterated exponential time, and beyond
We show that any language in nondeterministic time ((...(n))), where the...
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Computations with Greater Quantum Depth Are Strictly More Powerful (Relative to an Oracle)
A conjecture of Jozsa states that any polynomialtime quantum computatio...
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On the complexity of zero gap MIP*
The class MIP^* is the set of languages decidable by multiprover interac...
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A Parallel Repetition Theorem for the GHZ Game
We prove that parallel repetition of the (3player) GHZ game reduces the...
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Quantum Lovász Local Lemma: Shearer's Bound is Tight
Lovász Local Lemma (LLL) is a very powerful tool in combinatorics and pr...
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Quantum soundness of the classical low individual degree test
Low degree tests play an important role in classical complexity theory, ...
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UnWeyling the Clifford Hierarchy
The teleportation model of quantum computation introduced by Gottesman a...
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MIP*=RE
We show that the class MIP* of languages that can be decided by a classical verifier interacting with multiple allpowerful quantum provers sharing entanglement is equal to the class RE of recursively enumerable languages. Our proof builds upon the quantum lowdegree test of (Natarajan and Vidick, FOCS 2018) by integrating recent developments from (Natarajan and Wright, FOCS 2019) and combining them with the recursive compression framework of (Fitzsimons et al., STOC 2019). An immediate byproduct of our result is that there is an efficient reduction from the Halting Problem to the problem of deciding whether a twoplayer nonlocal game has entangled value 1 or at most 1/2. Using a known connection, undecidability of the entangled value implies a negative answer to Tsirelson's problem: we show, by providing an explicit example, that the closure C_qa of the set of quantum tensor product correlations is strictly included in the set C_qc of quantum commuting correlations. Following work of (Fritz, Rev. Math. Phys. 2012) and (Junge et al., J. Math. Phys. 2011) our results provide a refutation of Connes' embedding conjecture from the theory of von Neumann algebras.
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