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### Does the controlled Pauli Z gate cause entanglement?

Yes, CZ gate can entangle its inputs. For example $$CZ|+\rangle|+\rangle = \frac{|0\rangle|+\rangle+|1\rangle|-\rangle}{\sqrt2}$$ which is entangled because the reduced density matrix of either ...
• 15.6k
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• 15.6k
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### Can we express $\mathrm{tr}_A((A\otimes B)\rho_{AB})$ in terms of $A$, $B$, $\rho_A$ and $\rho_B$?

In general, the knowledge of the marginals $\rho_A$ and $\rho_B$ and the operators $A$ and $B$ is insufficient to compute $\mathrm{tr}_A((A\otimes B)\rho_{AB})$. Indeed, we can find two different ...
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### Prove that $|(\langle \psi|_{A} \otimes \langle \phi|_{B})|\theta\rangle_{AB}|^{2}<1$ for entangled $|\theta\rangle_{AB}$

TL;DR: There is no need to use Schmidt decomposition. The non-strict variant of the inequality follows directly from Cauchy-Schwarz inequality and equality is ruled out because $|\theta\rangle_{AB}$ ...
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### What is the best way to write a tridiagonal matrix as a linear combination of Pauli matrices?

Summary: There is a solution for expressing a tridiagonal matrix of the form you've provided for arbitrary $n$ in terms of Pauli operators using recursion. This procedure is given at the bottom of ...
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