On the quantum separability of qubit registers

We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed separability from cases in which entanglement depends on probability amplitudes. We provide closed-form support counts, identify forbidden configurations that enforce multipartite entanglement, and show how these results can enable fast entanglement diagnostics in quantum circuits. The framework offers immediate utility in classical simulation, entanglement-aware circuit design, and quantum error-correcting code analysis. This establishes support geometry as a practical and scalable tool for understanding entanglement in quantum information processing.

Source: arXiv:2601.15364v1 - http://arxiv.org/abs/2601.15364v1 PDF: https://arxiv.org/pdf/2601.15364v1 Original Link: http://arxiv.org/abs/2601.15364v1