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Results tagged with linear-algebra
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user 8265
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.
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 $$\frac12 (\left|1\right>\left<1\right| + \left|2\right>\left<2\right|)$$
- 476
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 …
- 476
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 …
- 476
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 …
- 476
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 …
- 476