{"id":"palomar/PALOMAR-2026-09-01-000003","url":"https://github.com/stalex444/werner-window/tree/81c70fe45f81da86c25254f3eb52123d504b452c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-01-000003-v1.json","repo":"https://github.com/stalex444/werner-window","tags":["quant-ph","math-ph","msc:81P40","msc:81P15","msc:81P16","quantum-information","entanglement","lean","bell-inequality"],"score":0,"title":"The entangled Born correlations: a mixed-state entanglement witness through the Born rule forced on the composite algebra","trust":"high","domain":"quant-ph","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"quant-ph","summary":"Kernel-checked entanglement package on the bipartite matrix algebra (2x2 tensor 2x2, native product index): (1) the separable-state CHSH bound 2 for the real-Pauli tuple, proved through the Bloch-disk constraint with no spectral theory; (2) an entanglement witness — a bipartite state, positive semidefinite with unit trace, that is NOT separable, with Born CHSH expectation equal to the Tsirelson value 2*sqrt(2) (the Bell state, exhibited explicitly in the Solution); (3) spectral projections without spectral theory — (1+W)/2 is an effect for every Hermitian involution W, any finite dimension;…","category":"research","comments":0,"disputed":false,"division":"physics","mentions":0,"verified":true,"discussed":0,"published":"2026-09-01","reactions":{},"formalized":true,"formalizes":[{"title":"Bell inequalities and the separability criterion","identifier":"Physics Letters A 271 (2000) 319-326","relationship":"formalizes"},{"title":"Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model","identifier":"Physical Review A 40 (1989) 4277-4281","relationship":"formalizes"},{"title":"Violating Bell inequality by mixed states: necessary and sufficient condition","identifier":"Physics Letters A 200 (1995) 340-344","relationship":"formalizes"}]}