Mixed-state quantum anomaly and multipartite entanglement

Abstract: Quantum entanglement measures of many-body states have been increasingly useful to characterize phases of matter. In this talk I will explore a surprising connection between mixed state entanglement and 't Hooft anomaly. More specifically, we consider lattice systems in d space dimensions with anomalous symmetry G where the anomaly is characterized by an invariant in group cohomology. We show that any mixed state ρ that is strongly symmetric under G, in the sense that Gρ~ρ, is necessarily (d+2)-nonseparable, i.e. is not the mixture of tensor products of (d+2) states in the Hilbert space. Furthermore, such states cannot be prepared from any (d+2)-separable states using finite-depth local quantum channels, so the nonseparability is long-ranged in nature. We provide proof of these results in d<2, and plausibility arguments in higher dimensions. The anomaly-nonseparability connection thus allows us to generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement, even in d=1.

HEP - phenomenologyHEP - theorymathematical physicscategory theory

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.