Timeline for How to prove there's no quantum channel that clones all classical states?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 8, 2024 at 16:27 | comment | added | Rammus | Question 2 is not an error. As I mention in the answer above, question 2 is solved by the quantum channel I wrote down (it is linear and is a quantum channel). It's just that specifically for pure states it happens to give the copied state you want) | |
| Mar 8, 2024 at 14:08 | comment | added | darkside | I am wondering if question 2 makes sense at all, since the linearity problem does not depend on the states being pure or classical the fact that $\Phi(\lambda \rho)=\lambda^2 \rho \otimes \rho$ is not the same as $\lambda \Phi(\rho)$ (unless $\lambda=0 or 1$) is still there for a pure and classical state (which are the states given by 2x2 matrices with 1 in the 1,1 entry and all zeros or in the 2,2 entry and all zetos). So is question 2 an error? | |
| Mar 8, 2024 at 14:05 | comment | added | Rammus | No your approach is not correct, you have written $\rho \oplus \rho$ and not $\rho \otimes \rho$. | |
| Mar 8, 2024 at 14:03 | comment | added | Rammus | If it is linear $\lambda \in \mathbb{C}$. | |
| Mar 8, 2024 at 11:07 | comment | added | darkside | Would my trace argument work in my try in the edit? | |
| Mar 8, 2024 at 10:55 | comment | added | darkside | is it real in [0,1] only? | |
| Mar 8, 2024 at 10:54 | comment | added | darkside | what is the range of values of lambda here? | |
| Mar 8, 2024 at 10:34 | history | answered | Rammus | CC BY-SA 4.0 |