QIF realizability of geometric bit-thread configurations

Determine whether every geometric bit-thread configuration admitted by the Headrick–Freedman framework admits a quantum-information-flow interpretation, or whether only a subset of such configurations can be lifted to QIF trajectories.

Background

The paper constructs geodesic-like QIF trajectories in the HaPPY tensor-network model by choosing microscopic ZX realizations of the AME cells compatibly with prescribed routes. This demonstrates that certain geometrically distinguished maximal bit-thread configurations can arise as projections of certified quantum-information-flow trajectories, but the construction depends on microscopic entanglement data not fixed by the perfect-tensor property alone.

The unresolved issue is whether this correspondence extends to the full set of geometric bit-thread configurations allowed by the Headrick–Freedman convex-optimization framework. A positive answer would give all such configurations a direct operational meaning in terms of quantum information flow and could allow geometric bit-thread data to constrain the microscopic entanglement structure of genuine holographic states.