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For questions about vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc.

2 votes
Accepted

How doesn't combining two eigenvectors that have the same eigenvalue for a specific matrix r...

There is no mistake. If you have a $2 \times 2$ matrix with one eigenvalue $\lambda$ and 2 linearly independent eigenvectors, then the whole plane is the eigenspace and the matrix is equal to $\lambda …
Vladimir Lysikov's user avatar
6 votes
Accepted

Finding the eigenvalues of a qutrit state

Maybe you forgot about the coefficient $\frac{1}{\sqrt{2}}$. The correct reduced density matrix is $$\frac12 (\left|1\right>\left<1\right| + \left|2\right>\left<2\right|)$$
Vladimir Lysikov's user avatar
4 votes
Accepted

How do you work out the matrix for controlled-U operations?

$\left|0\right>$ and $\left|1\right>$ don't mean $\begin{pmatrix}0 \\ 0\end{pmatrix}$ and $\begin{pmatrix}1 \\ 1\end{pmatrix}$. In bra-ket notation we usually fix some basis and denote by $\left|a\rig …
Vladimir Lysikov's user avatar
2 votes
Accepted

Quantum Phase Estimation answers distribution

Doublecheck your inverse QFT circuit. I get a distribution similar to yours if I put QFT instead of its inverse in the second part of the phase estimation algorithm. If the correct inverse QFT is used …
Vladimir Lysikov's user avatar
1 vote

Quantum Cryptography without Bell's Theorem -- Brassard - Bennett - Mermin

Whether the conjugation transposes tensor factors or not, I think, depends on the convention. The authors chose to write a bra in $(\mathcal{V} \otimes \mathcal{A})^*$ as $\left<a\right| \left<u\right …
Vladimir Lysikov's user avatar