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Results tagged with quantum-operation
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user 25170
For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.
3
votes
Accepted
What is the Choi matrix of the $H$ gate?
Let $\rho$ be your state.
Let $\mathcal{E}$ be the Hadamard map.
$$\therefore \mathcal{E}(\rho) = H \rho H^{\dagger} = H \rho H\;.$$
Let $\Upsilon_{\mathcal{E}}$ be the Choi matrix. For this case, $ …
- 2,593
11
votes
Accepted
What are "completely positive" and "CPTP" quantum maps?
[A]
States lie in Hilbert space $\mathcal{H_S}$.
$|\psi\rangle \in \mathcal{H_S}\,.$
Operators, density operators lie in the bounded operator space of $\mathcal{H}_S$.
$\rho \in \mathcal{B}(\mathca …
- 2,593
1
vote
When should I use the Choi matrix and when should I use the $\chi$ matrix?
This is just a comment, but it's too long for a comment, so writing as an answer. As I haven't read the paper you are asking about, I cannot answer as to particularly why that paper is using the proce …
- 2,593
5
votes
Resources for understanding non-unitary channels and operators
Lecture Notes on the Theory of Open Quantum Systems by Lidar
The Theory of Quantum Information by Watrous
Principles of
Quantum Communication Theory:
A Modern Approach by Khatri & Wilde
- 2,593
1
vote
Accepted
Physical description of trace of ancilla state yields a depolarising channel
You originally have the equation $(38)$. Then you calculate
$$\rho = U |0, \Omega_0 \rangle \langle 0,\Omega_0 | U^{\dagger}\,.$$
Taking the partial trace of $\rho$, $\text{Tr}_{\Omega}(\rho)$ will g …
- 2,593