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Thrice
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I'm trying to understand a part of the text where they prove QM doesn't satisfy Bell's inequality. I get how he derives the inequality. Apparently it's same as Sakuri (1985) and Townsend (2000). Problem is I lose him as soon as he starts the main part. Quoting almost directly,
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Consider a qubit oriented in an arbitrary direction. Consider a unit vector [tex]\vec{n} = \sin \theta \cos\phi \hat{x} + \sin \theta \sin\phi \hat{y} + \cos \theta \hat{z}[/tex]. The eigenvectors of [tex]\sigma \cdot \vec{n} [/tex] are..
[tex]|+_n \rangle = \cos \frac{\theta }{2} |0 \rangle + e^{i\phi }\cos \frac{\theta }{2} |1 \rangle[/tex]
[tex]|-_n \rangle = \cos \frac{\theta }{2} |0 \rangle - e^{i\phi }\cos \frac{\theta }{2} |1 \rangle[/tex]
He then goes on to interpret [tex]|\langle 0|+_n\rangle |^2[/tex] as a probability & i can follow from there. I just don't get the bit I posted. The hint is to consider the x & y axes, eg to get the eigenvectors of [tex]\sigma \cdot \hat{x} [/tex] set [tex]\theta =\pi /2[/tex] & [tex]\phi =0[/tex]
Thanks.
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Consider a qubit oriented in an arbitrary direction. Consider a unit vector [tex]\vec{n} = \sin \theta \cos\phi \hat{x} + \sin \theta \sin\phi \hat{y} + \cos \theta \hat{z}[/tex]. The eigenvectors of [tex]\sigma \cdot \vec{n} [/tex] are..
[tex]|+_n \rangle = \cos \frac{\theta }{2} |0 \rangle + e^{i\phi }\cos \frac{\theta }{2} |1 \rangle[/tex]
[tex]|-_n \rangle = \cos \frac{\theta }{2} |0 \rangle - e^{i\phi }\cos \frac{\theta }{2} |1 \rangle[/tex]
He then goes on to interpret [tex]|\langle 0|+_n\rangle |^2[/tex] as a probability & i can follow from there. I just don't get the bit I posted. The hint is to consider the x & y axes, eg to get the eigenvectors of [tex]\sigma \cdot \hat{x} [/tex] set [tex]\theta =\pi /2[/tex] & [tex]\phi =0[/tex]
Thanks.
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