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I have some ideas 1) Since $[\mathcal{O}^\dagger_A, \mathcal{O}] = - [\mathcal{O}_A, \mathcal{O}^\dagger]^\dagger$ and $\mathcal{O} = (\mathcal{O}+\mathcal{O}^\dagger)/2 + (\mathcal{O}-\mathcal{O}^\dagger)/2$ you can solve it only for self-adjoint operators $\mathcal{O}=\mathcal{O}^\dagger$. And even more, you can consider only real self-adjoint operators $... 4 This course was \$49 per course as verified certified learning outcome - a series of 3 courses + 1 more extra course on edX. Now the course has been taken down; at least no more new enrollments, and MITx Pro is offering it for \$2250 + \$2250 = \$4500. This is 20 times higher for the same course. I see there would be number of other MOOC coming soon. One ... 1 We can proceed by applying the parity check matrix$H_2$for$C_2^\perp$on the ancilla, which would become$\vert H_2(z'+e_2)\rangle =\vert H_2(z'+u + e_2 -u)\rangle =\vert H_2(e_2-u)\rangle$. Measuring the ancilla gives us$H_2(e_2-u)$. As$u$is known. we then know$H_2 e_2$, and in turn$e_2$. After correcting the now bit flip$e_2$, we have: $$\dfrac{1}{... 1 These are two separate questions, so I will (try to) answer them separately as well. Concerning the (reduction of) privacy in remote or cloud computing. Without any alterations, the instructions for a quantum computation that is to be run on a remote computer can be seen by that remote computer. That is to say, if you want to conceal the computations that ... 1 I don't believe that this is true (at least without further qualifiers). If I'm correctly understanding what you're trying to convey, I think we can essentially simplify this statement to asking whether there can exists a state |\psi\rangle and two projectors P_1 and P_2 such that$$P_1|\psi\rangle\neq P_2|\psi\rangle$$(ignoring normalisation for ... 3 I am not following all of the calculations in your post (for one thing because your first displayed equation does not mention$C_1$), but I know why the goal of the exercise is true. In fact it is true for any code at all, not just a CSS code. If$\mathcal{C} \subseteq \mathcal{H}_\text{qubit}^{\otimes n}$is any code, then you get an equivalent code$\...