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For questions about exercises or passages from the popular quantum computing textbook *Quantum Computation and Quantum Information* by Michael Nielsen and Isaac Chuang.

Part three (going by N&C page 544) states that $$tr(S(n)\rho^{\otimes n})=tr(S(n)\rho^{\otimes n}P(n,\epsilon))+tr(S(n)\rho^{\otimes n}(I-P(n,\epsilon))).$$ Now I understand how the term on the left o …
On page 547 of N&C, for $|\psi_{0}\rangle=|0\rangle$ and $|\psi_{1}\rangle=(|0\rangle+|1\rangle)/\sqrt{2}$ and for $|\tilde{0}\rangle=\cos(\pi/8)|0\rangle+\sin(\pi/8)|1\rangle$ and $|\tilde{1}\rangle= … asked Jul 13 '20 by GaussStrife Due to$\rho$being a positive and adjoint, you can always spectrally decompose it into a convex combination of pure states, it's eigenvectors. However, since the measurement statistics, or the action … answered Apr 16 '21 by GaussStrife 1answer On page 566, it states that using$S(\rho^{'})-S(\rho,\varepsilon) \ge S(\rho)$and combining this with$S(\rho) \ge S(\rho^{'})-S(\rho,\varepsilon))$, we get$S(\rho^{'})=S(\rho)-S(\rho,\varepsilon)$… asked Aug 10 '20 by GaussStrife 1answer On page 560, it states that$\$C^{(1)} \geq S(\frac{\varepsilon(|{\psi}\rangle\langle{\psi}|) +\varepsilon(|{\varphi}\rangle\langle{\varphi}|)}{2} - \frac{1}{2}\varepsilon(|{\psi}\rangle\langle{\psi}|) …