Squashed entanglement in one-dimensional quantum matter

Abstract

We introduce the concept of squashed entanglement between a system edges in one-dimensional quantum matter. We show that edge squashed entanglement discriminates unambiguously between topological insulators and topological superconductors by taking different quantized values, respectively to Bell-state entanglement and half Bell-state entanglement, depending on the statistics of the edge modes. Such topological squashed entanglement is robust under variations of the sample conditions due to disorder or local perturbations and scales exponentially with the size of a system, converging asymptotically to a quantized topological invariant also in the presence of interactions. By comparing it with the entanglement negativity, we show that topological squashed entanglement defines the natural measure of nonlocal correlation patterns in quantum matter. Finally, we discuss issues of experimental accessibility as well as possible generalizations to higher dimensions.