Spooky Action at a Distance
In 1935, Einstein, Podolsky, and Rosen argued that quantum mechanics must be incomplete because it predicted correlations between distant particles that seemed to require instantaneous influence. Einstein called it 'spooky action at a distance.' Decades later, John Bell showed these correlations could be tested experimentally, and Alain Aspect's 1982 experiments confirmed that quantum entanglement is real and cannot be explained by any local hidden variable theory.
Bell States and Maximally Entangled Pairs
The four Bell states are the simplest entangled systems. In |Φ+⟩ = (|00⟩+|11⟩)/√2, measuring one qubit as |0⟩ instantly projects the other into |0⟩, and similarly for |1⟩ — perfect correlation. The |Ψ-⟩ state gives perfect anti-correlation instead. These states are the building blocks for quantum teleportation, superdense coding, and entanglement-based quantum key distribution (E91 protocol).
CHSH Inequality and Nonlocality
The CHSH inequality provides a sharp boundary: if nature is described by local hidden variables, the correlation measure S cannot exceed 2. Quantum mechanics predicts S = 2√2 ≈ 2.83 for optimal measurement angles. This simulation lets you explore different angle choices and see the violation emerge. The optimal settings are α=0°, α'=45°, β=22.5°, β'=67.5° — try them to see the maximum violation.
Entanglement as a Resource
Modern quantum information theory treats entanglement as a quantifiable resource. Concurrence and entanglement entropy measure how entangled a state is. Bell states have maximum entanglement (concurrence = 1), while separable states have zero. Quantum computers consume entanglement to achieve speedups: algorithms like Shor's and Grover's require creating and manipulating highly entangled multi-qubit states throughout the computation.