Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am a student in the Netherlands, and I'll be attending university next year. However, I am doing some form of research on Quantum Computing with another student for our so-called "profielwerkstuk" but my understanding of Quantum Physics and math is sometimes not at the level that is needed. I am hoping some great person who does have the knowledge and skill to explain can help me with the following problem.

I have trouble understanding how the CHSH game, as described in this paper (and shortly explained in this post), works. I understand that 75% is the maximum probability of winning in a classical system. I understand the state given,

$$\frac{\left| 00 \right> + \left| 11 \right>}{\sqrt{2}}$$

As I understand this, this refers to 50% chance that both qubits are | 0>, and 50% chance that they are both | 1>. This can be prepared as such,

However, does this Bell State in the CHSH game lead to a probability of

$$\cos\left(\frac{1}{8}\pi\right)\approx0.85$$

I have made a visual representation of the Bloch Sphere from one side in Desmos, and I see how a certain angle corresponds to a certain probability. This might be completely incorrect and at the very least immensely incomplete, but this is how I picture a qubit.

How does the CHSH game conclude that the probability to 'win' in a quantum system is cos(1/8*pi), or an angle of 45° in my Desmos example?

Kind regards,

Isaiah van Hunen

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# B How does a Bell State lead to a probability in the CHSH game

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