Past exam of the quantum information course of the University of Cambridge / 2015 / Paper 1 / 2 / c

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Solution

The four required dot products are

a_{1} \cdot b_{1} = \frac{1}{2}, a_{1} \cdot b_{3} = - \frac{1}{2}, a_{3} \cdot b_{1} = \frac{1}{2}, a_{3} \cdot b_{3} = \frac{1}{2} .

(1)

Consequently the specified CHSH inequality combination is

S = - \frac{1}{2} - \frac{1}{2} - \frac{1}{2} - \frac{1}{2} = - 22 .

(2)

The magnitude reaches the quantum Tsirelson bound and exceeds the local bound two. The negative sign follows this singlet and the stated order of terms; other conventions can reverse it.

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Past exam of the quantum information course of the University of Cambridge / 2015 / Paper 1 / 2 / c

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