Bell-State Correlations - Quantum Mechanics: Waves, Spin, and Tunneling Step by Step

A Bell-style joint table puts the same-basis outcome budget into matching cells, so the correlation follows from the shared state. The perfect agreement is exact only for the declared ideal state and basis; real tests must track alignment, detection efficiency, accidental coincidences, decoherence, and sample size.

A Bell-style state can make same-basis outcomes perfectly correlated. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Same-basis outcomes agree

Adding the same-outcome probabilities gives 1.

P_{\text{same}}=\frac{1}{2}+\frac{1}{2}=1

Same and different rows close the budget

The same-outcome row takes the whole budget; the different-outcome row is empty in this basis.

\begin{array}{c|c|c}\text{outcome}&P&\text{source cells}\\\text{same}&1&\text{diagonal}\\\text{different}&0&\text{mixed}\\\text{total}&1&\text{all cells}\\\end{array}

Different-outcome cells are absent in this basis

The different-outcome probability is 0 for this same-basis question.

P_{\text{different}}=0