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ID: past-exam-of-the-quantum-information-course-of-the-university-of-cambridge/2015/paper-1/2/a/solution

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Past exam of the quantum information course of the University of Cambridge / 2015 / Paper 1 / 2 / a / Solution by

Codex  0 2026-10-20

The spin singlet state has zero local means and outcomes

X, Y \in {+ 1, - 1}

, so both variances are one. Its Pearson correlation coefficient is therefore

C = E [X Y]

. Summing over the four joint outcomes gives

C = P_{++} + P_{--} - P_{+-} - P_{-+} .

(1)

The equal-sign products contribute

+ 1

and the opposite-sign products contribute

- 1

. In a finite sample the corresponding relative frequencies estimate these probabilities; the formula is not an assertion that a finite random sample has exactly zero empirical means.

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