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Results tagged with linear-algebra
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user 5549
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.
-1
votes
Why do completely positive maps satisfy ${\rm Tr}[\Psi(\rho)_++\Psi(-\rho)_+]\leq{\rm Tr}[\P...
Edit: As pointed out by John Watrous again in the comments, the "proven" inequality is wrong so this answer is not correct.
$\def\braket#1{\langle{#1}\rangle}$I made a mistake in my first answer that …
- 331
1
vote
Accepted
A question on dimensions of the basis vectors for the $[[6,4]]$ code
$\underline{x} \in \mathbb{F}_{2}^{4}$ as you say, but $x_j \in \mathbb{F}_{2}$ is a scalar. $\underline{g_j}$ is a row of $G_{C/C^{\perp}}$, thus has length 6. Therefore, $\sum_{j=1}^{4}x_{j}\underli …
- 331
5
votes
Prove that if Kraus operators of $\Phi$ form an ONB then $\Phi$ is the replacement map
This solution uses the spectral theorem and some elementary linear algebra computations. If you let $P = \sum_{i = 1}^{d'} \lambda_i \vert{\psi_i}\rangle\langle{\psi_i}\vert$ be the spectral decomposi …
- 331