Speaker
Description
The NPA hierarchy, of Navascues, Pironio, and Acin, is a widely used tool for analyzing nonlocality across a range of settings in quantum information science. In the context of nonlocal games, this hierarchy of semidefinite programs (SDPs) provides a (non-increasing) sequence of upper bounds, converging (in the limit) to the commuting operator value. In fact, a corollary of the landmark MIP*=RE result employs the NPA hierarchy to conclude that there are nonlocal games for which the quantum (entangled) value is strictly less than the commuting operator value, providing a separation between the quantum and commuting operator models for quantum correlations. Despite much recent advancement, a fundamental question about the value of NPA hierarchy remained open. Given a nonlocal game, does there exist a (finite) level for which the NPA hierarchy attains the commuting operator value? Perhaps surprisingly, a positive and negative answer to this question is consistent with the recent undecidability results for the quantum and commuting operator values. In this talk, I will show that the above question has a negative answer. Moreover, I will discuss how the answer to the above question follows from a seemingly unrelated question about the computability of the commuting operator value.
| Keyword-1 | nonlocal games |
|---|---|
| Keyword-2 | quantum complexity classes |