Bell Test Experiments

Bell test experiments measure correlations between separated systems under different measurement settings and compare them with inequalities obeyed by local hidden-variable models. They test assumptions about locality, measurement settings, and pre-existing values; they are not merely demonstrations that entanglement exists.

Formula Hook

For binary outcomes with correlations $E(a,b)$, a standard CHSH combination is

$$S = E(a,b) + E(a,b') + E(a',b) - E(a',b').$$

Local hidden-variable models satisfying the CHSH assumptions obey

$$\left\lvert S\right\rvert\le2.$$

Quantum mechanics can reach

$$\left\lvert S\right\rvert \le 2\sqrt2,$$

and suitable entangled states and measurement settings violate the classical bound.

Canonical Home

This glossary entry is the current named-experiment home. For the state-theoretic bridge, see Entanglement and Foundations, Bell States, and Local Measurement Statistics. For classic citations, see Classic Papers.

Common Confusions

• Bell inequality violation does not enable controllable faster-than-light signaling.
• Entanglement and Bell violation are related but not identical; not every entangled mixed state violates a chosen Bell inequality.
• The theorem depends on clearly stated assumptions, not on a vague idea of “realism” alone.
• Experimental loopholes such as locality, detection, and setting independence must be addressed in real tests.

Related Entries

• Entanglement
• Density Matrix
• Decoherence

References

• J. S. Bell, “On the Einstein Podolsky Rosen Paradox,” Physics 1, 195-200, 1964.
• J. F. Clauser, M. A. Horne, A. Shimony, and R. A. Holt, “Proposed Experiment to Test Local Hidden-Variable Theories,” Physical Review Letters 23, 880-884, 1969.
• A. Aspect, J. Dalibard, and G. Roger, “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers,” Physical Review Letters 49, 1804-1807, 1982.
• B. Hensen et al., “Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres,” Nature 526, 682-686, 2015.