Questions tagged [quantum-operation]
For questions about quantum channels or more generally quantum maps and the related formalism. For questions about unitary operations, please use quantum-gate instead.
5 questions from the last 30 days
1
vote
1
answer
129
views
What does the inequality $\sum_k A_k^* A_k \leq I$ represent in Kraus' theorem?
Nielsen and Chuang's statement of Kraus' Theorem includes the inequality
$$ \sum_k A_k^* A_k \leq I.$$
What does this inequality represent? What quantities are being compared by this symbol?
- 37
2
votes
0
answers
84
views
Finding solutions to commutation relation
In a Hilbert space of dimension $d$, a positive definite operator $A>0$ is given. I would be interested in the set of operators $B>0$ such that there exists some $C>0$ that satisfies:
$$i[A,B]...
- 121
3
votes
0
answers
47
views
Reset channels for two-qubit space
In the paper "Unbiased Simulation of Near-Clifford Quantum Circuits" by Ryan S. Bennink et al. (arXiv) the authors define a Pauli reset ("Pauli measurements followed by Clifford ...
- 764
1
vote
0
answers
112
views
Improving the Bound on $\|\Phi^k[\mathbf{I}_d] - \Phi^{k+1}[\mathbf{I}_d]\|$ for a CP Map
I am analyzing a completely positive (CP) linear map $\Phi : \mathbb{R}^{d \times d} \to \mathbb{R}^{d \times d}$ with the following properties:
$\Phi[\mathbf{I}_d] \preccurlyeq \mathbf{I}_d$,
All ...
- 11
1
vote
1
answer
33
views
How to obtain $U$, representing the action of the amplitude dampening channel?
How to obtain $U$ for the amplitude dampening channel?
The behaviour of the amplitude damping channel on the system can be represented by $U$, a unitary matrix which has the following effect:
$U|00\...
- 739