The NPA hierarchy does not always attain the commuting operator value
By: Marco Fanizza , Larissa Kroell , Arthur Mehta and more
Potential Business Impact:
Proves some math problems are impossible to solve.
We show that it is undecidable to determine whether the commuting operator value of a nonlocal game is strictly greater than 1/2. As a corollary, there is a boolean constraint system (BCS) game for which the value of the Navascu\'es-Pironio-Ac\'in (NPA) hierarchy does not attain the commuting operator value at any finite level. Our contribution involves establishing a computable mapping from Turing machines to BCS nonlocal games in which the halting property of the machine is encoded as a decision problem for the commuting operator value of the game. Our techniques are algebraic and distinct from those used to establish MIP*=RE.
Similar Papers
The NPA hierarchy does not always attain the commuting operator value
Quantum Physics
Proves some math problems are impossible to solve.
Quantitative Quantum Soundness for Bipartite Compiled Bell Games via the Sequential NPA Hierarchy
Quantum Physics
Makes secret computer codes work without special machines.
Bounding the asymptotic quantum value of all multipartite compiled non-local games
Quantum Physics
Makes quantum computers understand complex games better.