An Exact Entanglement-Breaking Index for the Explicit 21-Dimensional PPT-Square Counterexample
Year: 2026
Type: preprint
Abstract: We establish that the explicit trace-preserving 21-dimensional PPT channel constructed in OpenAI's September 2026 Entanglement with zero distillable secret key in local dimension ten has entanglement-breaking index exactly three. The original paper proves that its square is not entanglement breaking; we give an exact finite certificate that its cube is entanglement breaking. The certificate proves the reverse-order constituent composition is entanglement breaking, using rational invertible local filters, strict diagonal dominance, partial-transpose invariance, and an exact nonnegative decomposition into 666 real product projectors. A self-contained integer-only Python verifier and the LaTeX source are included as a supplementary ZIP. This result determines the index of one specific channel; it does not resolve the universal PPT-cubed conjecture. The work is a preprint and has not been independently peer reviewed. The structured Related works identify the original construction, Park's eventual entanglement-breaking theorem, and an earlier qubit-intermediate PPT composition result by Henry.
Author: Henry, Kias
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225378176