Squashed entanglement in one-dimensional quantum matter

TL;DR

This paper introduces a new measure based on quantum conditional mutual information to characterize topological phases in one-dimensional quantum systems, demonstrating its robustness and potential as a topological invariant.

Contribution

The authors define quantum conditional mutual information between edges in 1D quantum systems and show it characterizes topological phases, linking it to squashed entanglement and providing analytical support.

Findings

Edge-to-edge quantum conditional mutual information distinguishes topological from trivial phases.

This measure converges exponentially to a quantized invariant, even with disorder and interactions.

It correlates with squashed entanglement, offering a precise characterization of nonlocal correlations.

Abstract

Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipartitions. As such, they are sensitive to the fine-grain structure of quantum systems. Building on this observation, we introduce the concept of quantum conditional mutual information between the edges of quantum many-body systems. We show that this quantity characterizes unambiguously one-dimensional topological insulators and superconductors, being equal to Bell-state entanglement in the former and to half Bell-state entanglement in the latter, mirroring the different statistics of the edge modes in the two systems. The edge-to-edge quantum conditional mutual information is robust in the presence of disorder or local perturbations, converges exponentially with the system size to a quantized topological invariant, even in the presence of interactions, and vanishes in the trivial phase. We thus conjecture that it coincides with the edge-to-edge squashed entanglement in the entire ground-state phase diagram of symmetry-protected topological systems, and we provide some analytical evidence supporting the claim. By comparing them with the entanglement negativity, we collect further indications that the quantum conditional mutual information and the squashed entanglement provide a very accurate characterization of nonlocal correlation patterns in one-dimensional quantum matter.