Entangled benchmarks for local-profile approximation

Construct an alternative conditioning approximation for arbitrary quantum state classes that approximates their local Pauli profiles by states in the convex hull of a suitable entangled benchmark, with errors small enough to produce a useful energy comparison for Hamiltonian models where separable approximations are inadequate.

Background

The conditioning construction developed in the paper replaces a state's conditional marginals by products, thereby producing separable approximations and enabling comparisons with product-state benchmarks. This framework is effective for the dense quantum p-spin model and for several structured state classes.

The authors leave unresolved whether the same strategy can preserve suitable entanglement in the benchmark states. Such a construction could extend the local-profile complexity method to Hamiltonian models for which approximation by separable states does not provide sufficient control.