10 votes

Is there a comprehensive list of counterexamples in quantum information?

A few weeks ago I launched a little side project of mine: a google document on Counterexamples in Quantum Information The idea was to have a centralized document acting as a reference work for ...
Frederik vom Ende's user avatar
8 votes
Accepted

How can the depolarizing channel be a quantum operation?

The correct linear form of the depolarizing channel is $$ \varepsilon(\rho) = (1-p)\rho + p\frac{I}{2}{\rm Tr}(\rho). $$ For density matrices ${\rm Tr}(\rho)=1$, so you can usually see the form ...
Danylo Y's user avatar
  • 7,289
3 votes

$M(\rho)=\operatorname{Tr}_2[U(\rho\otimes\rho_2)U^{\dagger}]$ is unitary $\iff U=U_1\otimes U_2$, a product of $2$ unitary operators?

To add to the other nice answers as well as John Watrous' great counterexample: Interestingly one can characterize when "$\operatorname{Tr}_2(U(\rho\otimes\omega)U^{\dagger})$ is a unitary ...
Frederik vom Ende's user avatar
2 votes

Are quantum channels bounded linear maps?

To complement Danylo's great answer, let me go into a bit more details about the infinite-dimensional case and point out that the correct extension of a channel $\mathcal{N}:D(\mathcal{H}_A) \...
Frederik vom Ende's user avatar
1 vote
Accepted

Interconversion between different representations of quantum channels

The only question which I believe has not been addressed by the comments yet is your question 3: how is the Stinespring representation related to the representation matrix $K(\Phi)$ of $\Phi$? To ...
Frederik vom Ende's user avatar
1 vote

Matrix Representation of Quantum Channels

In your latest comments you talked about matrices (channels) that meet some commutation relations. This is best tackled with the representation matrix with respect to vectorization---as linked in one ...
Frederik vom Ende's user avatar

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