SWhat changed
Every finite-dimensional bipartite separable state has positive partial transpose. The Horodecki positive-map characterization proves that this necessary test is also sufficient for 2x2 and 2x3 systems; in general separability is equivalent to positivity after applying every positive map to one subsystem.
Scientific scope
Every finite-dimensional bipartite separable state has positive partial transpose. The Horodecki positive-map characterization proves that this necessary test is also sufficient for 2x2 and 2x3 systems; in general separability is equivalent to positivity after applying every positive map to one subsystem. PPT is not sufficient in unrestricted higher dimensions. Testing only completely positive maps cannot characterize entanglement. Entanglement detection is not equivalent to a universal Bell-inequality violation test. The two original papers have distinct one-author and three-author bylines; low-dimensional positive-map decomposition uses earlier operator-algebra results.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. PPT is not sufficient in unrestricted higher dimensions. Testing only completely positive maps cannot characterize entanglement. Entanglement detection is not equivalent to a universal Bell-inequality violation test. The two original papers have distinct one-author and three-author bylines; low-dimensional positive-map decomposition uses earlier operator-algebra results.
Contributors
- The named authors in the research record · SCIENCE: The original named human researchers developed the exact mathematical construction or framework. Composite source families retain separate original paper bylines and predecessor roles; they are not a fictional joint publication. Individual effort shares, person identity joins and nationalities are not inferred. The source reading is not independent proof certification.
- Separability Criterion for Density Matrices
- Separability of mixed states: necessary and sufficient conditions
Provisional WRS assessment, edition 2026-10-23.9. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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