Entanglement Reference Sheet — E(Δ) = −V·cos Δ

🎛 Controls

Visibility V (0…1): 1.00

A0 (°): 0.0

A1 (°): 45.0

B0 (°): 22.5

B1 (°): 67.5

Δ = A0–B0 = 22.5° status

Correlation E(A0,B0)

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S (CHSH)

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CHSH game win prob

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Regime: – Local ≤ 2 • Quantum ≤ 2√2 • PR = 4

📊 Joint Distribution & Fisher Information

Single-pair angle Δ (°) for E & P(a,b): 22.5

Δ direct input (°)

E(Δ)

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Fisher 𝓕(Δ)

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Max 𝓕 over Δ

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Bars show joint probabilities P(++), P(+−), P(−+), P(−−) with fair marginals (no-signaling). Computed via P(a,b)=¼(1+a b·E). Marginals: P(a=+1)=0.5000, P(b=+1)=0.5000.

🔗 Monogamy Check (Toner–Verstraete)

Enter candidate S_AC

S_AB = – S_AC = – Sum = – Status: –

📚 Comparison Table

Model	Max CHSH S	Correlation form	Signaling?
Local Hidden Variables	≤ 2	Piecewise linear	No
Quantum (this work)	≤ 2√2 ≈ 2.828	`E(Δ)=−V cos Δ`	No
PR-Box (supra-quantum)	4	±1 (discontinuous)	No

Information causality rules out PR-box correlations; rotational symmetry fixes the cosine form; maximum entropy selects the unique joint distribution.