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### How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?

If you consider the state $$\Omega_- = \frac{1}{\sqrt{2}}(|00\rangle + |11\rangle).\tag{1}$$ you will find that there is NO violation. Let me show this. Note that the approach I will use for solving ...
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### Why is a density matrix an orthogonal projector?

If a matrix is a projector, it squares to itself. So, you just have to verify that $\rho^2=\rho$. You'll need the assumption that the length of the Bloch vector is 1.
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### How to know what eigenvalue corresponds to measurements of individual qubits in a multiqubit system?

From your current description, it seems that you have found each eigenvector $\{|v_1\rangle,...,|v_4\rangle\}$ and its associated eigenvalue $\lambda_1,...,\lambda_4$. These eigenvalues represent the ...
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You can find the single-qubit expectation values by tracing out the degrees of freedom of the other qubit. Mathematically, this corresponds to $\rho_A = \text{Tr}_B(|{\psi}_{AB}\rangle\langle{\psi_{AB}... 4 votes Accepted ### What is the expression for$|\psi\rangle\!\langle\psi|$if$|\psi\rangle=\cos(\theta/2)|0\rangle+\sin(\theta/2)e^{i\phi}|1\rangle$? You are missing the fact that $$\langle \psi | = \bigg( |\psi\rangle \bigg)^{\dagger} \,.$$ "$\langle \psi|$" is conjugate transpose of "$|\psi\rangle$". So, if$\$|\psi\rangle = \...

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