Institute for Quantum Information Seminar

The fact that non commuting physical observables are at the base of quantum mechanics is a well known for many years now. In this talk I'll examine the converse problem - how quantum can commuting systems be - from a computational-theoretic point of view. Specifically, I'll present a recent result with Dorit Aharonov that the commuting local Hamiltonian problem is in NP for a wider range of Hamiltonian locality than previously known. As a corollary of this fact we achieve a tight bound between commuting local Hamiltonian systems that can give rise only to local entanglement, and commuting systems that can allow non-local entanglement, namely Topologically-ordered systems.