Quantum Lunch: The martingale method meets the detectability lemma
Speaker: Angelo Lucia
The martingale method meets the detectability lemma
When we analyse quantum many-body Hamiltonians for
The detectability lemma is a tool developed in the context of quantum Hamiltonian complexity theory, with a very strong combinatorics flavour, and has used between other things to improve the area law bound for gapped Hamiltonians. Recently a converse detectability lemma has appeared, used for spectral gap amplification.
I would like to present the connection between these two lemmas, by presenting a different proof of the martingale method, in order to see it from a more "information theoretic" point of view, and making it more slightly natural for higher dimensions. Under this reformulation, it will be clear that the converse detectability implies a condition similar, but weaker, than the assumption of the martingale method. Moreover,