Quantum entanglement: correlations in random outcomes
Before you start
Each side sees apparently random outcomes. Why can comparing the pairs reveal a distinctive pattern? “One up, the other down” alone is not enough to establish entanglement—changing measurement settings is essential.
The setupA central source emits spin-½ pairs; a singlet is a paired state with total spin zero. Alice and Bob select measurement axes independently. Detectors record ± outcomes; the squares retain local records, compared after ordinary communication.
What to do and noticeMeasure a singlet along the same axis: opposite outcomes, with each local sign still about equally likely. · Compare the entangled state with a classical ±z mixture, then turn both measurement axes. · In the optional advanced experiment, randomly choose four setting pairs and compare CHSH S with the local hidden-variable bound of 2.
Predict firstCan Alice read Bob’s setting from her own outcomes alone?
Distinguish local randomness, paired correlations and the impossibility of faster-than-light signalling.
Prerequisites: First try Spin & measurement: a spin-½ measurement along one axis has + and − outcomes.Start with local records
Predict firstCan Alice read Bob’s setting from her own outcomes alone?
No. For a singlet, each local sign has probability ½, independent of the other party’s axis. Correlations appear only when corresponding records are compared.
How to observe
- Measure a singlet along the same axis: opposite outcomes, with each local sign still about equally likely.
- Compare the entangled state with a classical ±z mixture, then turn both measurement axes.
- In the optional advanced experiment, randomly choose four setting pairs and compare CHSH S with the local hidden-variable bound of 2.
Model notes
This samples theoretical probabilities; it is not a real Bell experiment or an animation of a hidden mechanism. Colours only label records. Finite samples fluctuate: one value above 2 does not replace statistical significance or experimental loophole analysis. Paths are apparatus schematics; local outcomes cannot be controlled to send a faster-than-light message.