Understanding Quantum Many-Body Theory

Roy J. Garcia, Kaifeng Bu, Liyuan Chen +1 more

The study of state revivals has long advanced our understanding of dynamical systems. We introduce a resource theory framework to study the use of state revivals in quantum information. In this theory, a state is said to contain no amount of resource if it experiences perfect revivals under some unitary evolution. All other states are said to be resourceful. The resource, which we dub ``nonrevivals,'' quantifies a state's inability to experience revivals. We use our framework to understand revivals in quantum many-body scarred systems and their applications. In particular, we show that quantum many-body scarred dynamics can produce revivals in the Hayden-Preskill decoding protocol and can also be used to recover damaged quantum information. We also use our resource theory to bound information scrambling. Our theory establishes a framework to study information retrieval and its applications in quantum many-body physics.

Alexandre M. Zagoskin

Alexandre M. Zagoskin

W. Jim Neidhardt

An elementary approach is presented to the many-body formalism needed to understand simple models of superfluid systems. In the framework of occupation number space-particle conserving operators that represent single-body and two-body observables are constructed in an intuitive manner. It is then shown that this formalism when applied to such observables as single-particle energy and two-body interaction potential yields results which are physically plausible. The basic formalism for the understanding of many-body systems is thereby presented without recourse to a complete development of quantum field theory.

Adán Cabello

Quantum n-body correlations cannot be explained with (n-1)-body nonlocality. However, this genuine n-body nonlocality cannot surpass certain bounds. Here we address the problem of identifying the principles responsible for these bounds. We show that, for any n≥2, the exclusivity principle, as derived from axioms about sharp measurements, and a technical assumption give the exact bounds predicted by quantum theory. This provides a unified explanation of the bounds of single-body contextuality and n-body nonlocality, and connects two programs towards understanding quantum theory.

Laurens Vanderstraeten