Entanglement generated by non-ladder QCD kernels

Determine whether crossed-box, self-energy, and Dyson–Schwinger-based non-ladder Bethe–Salpeter kernels produce volume-law entanglement in the qubit encoding of the Bethe–Salpeter equation.

Background

The paper studies the homogeneous Bethe–Salpeter equation for two relativistic scalar particles in the ladder approximation after Wick rotation, O(4) S-wave projection, and qubit encoding. For this restricted problem, the dominant Bethe–Salpeter amplitude exhibits low, area-law-like entanglement and is efficiently represented by low-bond-dimension matrix-product states, which limits the prospect of quantum advantage.

The authors identify non-ladder kernels in QCD as a physically motivated extension that may generate substantially stronger correlations. Such kernels include crossed-box and self-energy contributions, as well as dressed kernels derived from Dyson–Schwinger equations. The unresolved issue is whether these additional interactions change the entanglement structure of the qubit-encoded Bethe–Salpeter amplitude sufficiently to produce volume-law entanglement, potentially making classical tensor-network methods ineffective and quantum advantage more plausible.