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3.3: The Einstein-Podolsky-Rosen "Paradox"
https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_III_(Chong)/03%3A_Quantum_Entanglement/3.03%3A_The_Einstein-Podolsky-Rosen_Paradox
In the basis of spin-up and spin-down states, the operator $\hat{S}_x$ has matrix representation $\hat{S}_x = \frac{\hbar}{2}\, \begin{pmatrix}0&1\\1&0\end{pmatrix}.$ The eigenvalues and eigenvect...In the basis of spin-up and spin-down states, the operator $\hat{S}_x$ has matrix representation $\hat{S}_x = \frac{\hbar}{2}\, \begin{pmatrix}0&1\\1&0\end{pmatrix}.$ The eigenvalues and eigenvectors are $\begin{align} \begin{aligned}s_x = \;\;\frac{\hbar}{2},\; &\;\;\; |\!+\!x\rangle = \frac{1}{\sqrt{2}}\Big(|\!+\!z\rangle + |\!-\!z\rangle\Big) \\ s_x = -\frac{\hbar}{2}, &\;\;\; |\!-\!x\rangle = \frac{1}{\sqrt{2}}\Big(|\!+\!z\rangle - |\!-\!z\rangle\Big).\end{aligned}\end{align}$ Convers…

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