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facenian
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It seems that the upper bound of the CHSH inequality is ##2\sqrt{2}##
How is it analytically derived?
How is it analytically derived?
facenian said:It seems that the upper bound of the CHSH inequality is ##2\sqrt{2}##
How is it analytically derived?
I'm sorry I did not express it correctly. I was talking about the quantum mechanical bound not the hidden variable bound.stevendaryl said:That's not an upper bound of the CHSH inequality. The upper bound is 2. The fact that actual correlations are [itex]2\sqrt{2}[/itex] shows that the inequality is violated by QM.
facenian said:Excellent! Thank you very much.
There is one more question however, since 2 and -2 occur it seems that ##-2\sqrt{2}## should also appear.
Yes, and it is only a minor detail. I seems reasonable to accept only solutions in the range ##[0,2\pi]## so maybe instead of ##B=\pi-A## putting ##B=\pi\pm A## will sufficestevendaryl said:Just trying some values, I found that there is a minimum at [itex]\alpha = \gamma = \frac{\pi}{4}, \beta = \frac{7\pi}{4}[/itex], and that gives:
[itex]C(\alpha, \beta, \gamma) = -2 \sqrt{2}[/itex]
So, it looks I should have used a more general condition:
- If [itex]sin(A) = sin(B)[/itex], then either [itex]B = A + 2n\pi[/itex] or [itex]B = (2n+1)\pi - A[/itex]
- If [itex]sin(A) = -sin(B)[/itex], then either [itex]B = A + (2n+1)\pi[/itex] or [itex]B = 2n\pi - A[/itex]
The CHSH violation bound in computing refers to a measure of the maximum violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality that can be achieved in a quantum experiment. It is a key parameter used in quantum information and cryptography to quantify the strength of quantum correlations between two distant systems.
The CHSH violation bound is calculated by performing a CHSH test, which involves measuring the correlations between two quantum systems using a series of four measurements. The results of these measurements are then used to calculate the CHSH inequality, which can be compared to the theoretical maximum value to determine the CHSH violation bound.
The CHSH violation bound is significant in quantum computing because it provides a quantitative measure of the amount of entanglement present in a quantum system. It is also used in the development of quantum protocols, such as quantum teleportation and quantum key distribution, and is essential for ensuring the security of these protocols.
Yes, the CHSH violation bound can be exceeded in certain quantum systems, which are known as nonlocal systems. These systems exhibit stronger correlations between two distant particles than is allowed by classical physics, and their CHSH violation bound can reach the maximum value of 2√2.
In quantum cryptography, the CHSH violation bound is used to test the security of quantum key distribution protocols. By comparing the measured CHSH violation bound to the theoretical maximum value, it can be determined whether the quantum system is secure against eavesdropping attempts. If the CHSH violation bound exceeds the theoretical maximum, this indicates that the system is secure and that the quantum key can be used for secure communication.