New answers tagged quantum-operation
2
votes
Accepted
How to extract probabilities from Kraus representation?
We can indeed rewrite $\mathcal{E}(\rho)=\sum_iK_i\rho K_i^\dagger$ as $\mathcal{E}(\rho)=\sum_ip(i)\rho_i$ by setting $p(i):=\mathrm{tr}(K_i\rho K_i^\dagger)$ and $\rho_i:=\frac{K_i\rho K_i^\dagger}{...
- 18.2k
0
votes
Is the Eastin-Knill Theorem incorrect?
$ \mathcal{G} $ is a closed subgroup of $ \mathcal{T} $, which is a closed subset of a unitary group. Unitary groups are compact. Closed subsets of compact spaces are compact. Thus $ \mathcal{G} $ is ...
- 2,158
2
votes
What are examples of quantum maps with complex eigenvalues?
You can slightly modify that example for $d=2$.
Take $\Phi(E_{11}) = (E_{11}+I)/3$, $\Phi(E_{22}) = (E_{22}+I)/3$, but $\Phi(E_{12}) = iE_{12}/3$, $\Phi(E_{21}) = -iE_{21}/3$, where $E_{ij}$ are ...
- 6,353
0
votes
Understanding of the transverse-field Ising model
Your Hamiltonian is not transverse.
In your Hamiltonian, your magnetic field monomial $-\sum_{i}h_{i}\sigma_{i}^{z}$ is in the same direction as (longitudinal with) your interaction terms $-\sum_{ij}...
- 8,926
4
votes
Accepted
What is the meaning of $\langle e_k|U|e_0\rangle$ when $U$ acts on a larger Hilbert space than that in which $|e_0\rangle$ and $|e_k\rangle$ live?
TL;DR: We can understand the object $E_k=\langle e_k|U|e_0\rangle$ rigorously in two steps. First, think of $\langle e_k|$ and $|e_0\rangle$ as linear functions. Next, treat the implicit operation in $...
- 18.2k
Top 50 recent answers are included