feat: strip domain cards, add physics-only examples (depolarising noise, quantum switch)

Author: dcoldeira

index.html

@@ -992,28 +992,15 @@ <h2>What people ask Bell</h2>
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         <div class="example-card">
-          <div class="example-domain">Quantum Biology</div>
-          <div class="example-q">"Does quantum coherence in the FMO photosynthetic complex contribute to energy transfer efficiency?"</div>
-          <div class="example-a">FMO complex (7 chromophores): coherence lifetime = <strong>300 fs</strong> at 77K. Quantum transfer efficiency <strong>94.2%</strong> vs 71.3% classical. Phonon-assisted transport accounts for the 32% advantage.</div>
+          <div class="example-domain">Quantum channels</div>
+          <div class="example-q">"If a Bell state passes through a depolarising channel with p = 0.3, does it still violate the Bell inequality?"</div>
+          <div class="example-a">S(p=0.3) = <strong>2.404</strong> — Bell inequality still violated (classical bound = 2.0). Violation persists for p &lt; 0.5. At p = 0.5: S = 2.0, threshold crossed.</div>
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         <div class="example-card">
-          <div class="example-domain">Quantum Sensing</div>
-          <div class="example-q">"Can entangled atoms beat the standard quantum limit for measuring tiny magnetic fields?"</div>
-          <div class="example-a">GHZ state, n=100 atoms: QFI = <strong>10,000</strong> (Heisenberg scaling n²). Cramér-Rao bound δφ = 0.01 rad. SQL = 0.1 rad. Quantum advantage = <strong>10×</strong> — at Heisenberg limit.</div>
-        </div>
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-        <div class="example-card">
-          <div class="example-domain">Quantum Chemistry</div>
-          <div class="example-q">"What is the orbital entanglement in H₂ at equilibrium, and how does it change as I stretch the bond?"</div>
-          <div class="example-a">H₂ STO-3G: E_FCI = <strong>−1.137 Ha</strong> at R = 0.74 Å. Orbital entanglement = <strong>0.196 bits</strong> (equilibrium) → <strong>1.99 bits</strong> at dissociation. Correlation energy = −20.5 mHa. Bond breaking is a quantum phase transition in orbital entanglement space.</div>
-        </div>
-
-        <div class="example-card coming-soon">
-          <span class="coming-badge">Coming soon</span>
-          <div class="example-domain">Materials Science</div>
-          <div class="example-q">"Is this 2D lattice in a topologically non-trivial phase? Where is the quantum phase transition?"</div>
-          <div class="example-a">Compute entanglement spectrum and topological invariants of a 2D Hubbard model. Detect phase boundaries via long-range entanglement signatures.</div>
+          <div class="example-domain">Indefinite causal order</div>
+          <div class="example-q">"Can a quantum switch with indefinite causal order transmit information through two completely depolarising channels?"</div>
+          <div class="example-a">Fixed order: capacity = <strong>0 bits/use</strong> (both channels fully depolarising). Quantum switch: capacity &gt; 0 — indefinite causal order activates a classically forbidden channel.</div>
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