What Are Bell States and Their Role in Spin Angular Momentum Conservation?

[RUTA]

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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