Study proves entanglement breaking in PPT maps using qubit systems, suggesting implications for quantum theory.
We prove that the composition of two PPT maps through an intermediate qubit system is entanglement breaking. Specifically, for arbitrary finite dimensions m and n, if Φ: Mₘ → M₂ and Ψ: M₂ → Mₙ are completely positive and completely copositive, then Ψ ∘ Φ is entanglement breaking. The proof uses the special 2 × 2 block structure imposed by the qubit intermediate system, Schur-complement inequalities, an operator interpolation argument, and an explicit separability decomposition. As a consequence, no counterexample to the PPT-squared conjecture can occur through the 4 → 2 → 4 composition pattern.
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Kias Henry (2026) studied this question.
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