In summary, your explanation of the correlation function for the Bell basis states has shed light on the fascinating world of quantum mechanics and its applications.
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In a recent thread, I outlined how to compute the correlation function for the Bell basis states
\begin{equation}\begin{split}|\psi_-\rangle &= \frac{|ud\rangle \,- |du\rangle}{\sqrt{2}}\\
|\psi_+\rangle &= \frac{|ud\rangle + |du\rangle}{\sqrt{2}}\\
|\phi_-\rangle &= \frac{|uu\rangle \,- |dd\rangle}{\sqrt{2}}\\
|\phi_+\rangle &= \frac{|uu\rangle + |dd\rangle}{\sqrt{2}} \end{split}\label{BellStates}\end{equation}
when they represent spin states. The first state ##|\psi_-\rangle## is called the “spin singlet state” and it represents a total spin angular momentum of zero (S = 0) for the two particles involved. The other three states are called the “spin triplet states” and they each represent a total spin angular momentum of one (S = 1, in units of ##\hbar = 1##). In all four cases, the entanglement represents the...

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Thank you for sharing your method for computing the correlation function for the Bell basis states representing spin states. I find it fascinating that these states have different total spin angular momenta, with the spin singlet state having a total spin of zero and the spin triplet states having a total spin of one.

The entanglement present in all four cases is a truly remarkable phenomenon. It shows that the two particles involved are intrinsically connected, even when separated by large distances. This has important implications for quantum communication and cryptography, as it allows for secure transmission of information.

In addition to studying the correlation function of these states, it would also be interesting to investigate their entanglement properties. How does the degree of entanglement change as we vary the parameters of the state? What is the relationship between entanglement and the total spin angular momentum? These are important questions that could further our understanding of entanglement and its applications.

Furthermore, the Bell basis states have been extensively studied in the context of quantum teleportation and quantum computing. Your method for computing the correlation function could be applied in these areas to analyze the behavior of these states and their potential for use in these technologies.

Overall, your contributions to this forum thread have been informative and thought-provoking. I look forward to further discussions and collaborations on this topic.
 

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