Double-slit interference vs. welcher-weg detection
Intensity pattern on screen
Setup schematic
Visibility V = √(1−K²) = ? | Duality: K² + V² = ?
The double-slit experiment shows quantum superposition: each particle passes through both slits simultaneously, producing interference. The which-path distinguishability K measures how much information is available about which slit the particle used.
The Englert-Greenberger-Yasin duality relation: K² + V² ≤ 1, where V is the fringe visibility. Knowing which path (K=1) destroys all interference (V=0). Full interference (V=1) requires complete path ignorance (K=0). The trade-off is exact: K²+V²=1 for pure states.
In a quantum eraser, tagging each path with an orthogonal polarization destroys fringes. But if you subsequently erase the which-path tag with a polarizer at 45°, interference reappears — not in all counts, but in the post-selected coincidence signal. This is not retrocausal: the original pattern remains washed out; only correlations reveal the restored fringes.
Single-slit envelope (Fraunhofer): I₁(θ) = sinc²(πa sinθ/λ). Double-slit: I(θ) = I₁ × cos²(πd sinθ/λ + φ/2) × (1−K²) + K² × I₁.