Timeline for What is the most general quantum operation that preserves the marginal?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 15, 2021 at 10:12 | vote | accept | JRT | ||
| Mar 12, 2021 at 20:53 | answer | added | Adam Zalcman | timeline score: 3 | |
| Mar 11, 2021 at 3:18 | comment | added | JRT | @gIS I'm asking if for any $\rho, \sigma$ such that $\rho_A = \sigma_A$, can we restrict the map $\Phi: \mathcal{H}_{ABC}\rightarrow\mathcal{H}_{ABC}$ that achieves $\Phi(\rho) = \sigma$ to a form like $I_A\otimes U_{BC}$? | |
| Mar 10, 2021 at 11:37 | comment | added | glS♦ | are you asking for the class of maps (or channels?) $\Phi$ such that $\mathrm{Tr}_2[\Phi(\rho)]=\mathrm{Tr}_2[\Phi(\sigma)]$ for all $\rho,\sigma$, or only the class of maps (channels) preserving the marginals of two specific states? | |
| Mar 10, 2021 at 11:35 | history | edited | glS♦ | CC BY-SA 4.0 |
edited title
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| Mar 10, 2021 at 9:42 | comment | added | JRT | @Rammus good point. So I guess the question is whether I can still achieve the transformation using $I_A$ or if there are cases where the transformation requires me to use a unitary $U_A$ with the properties you've pointed out. | |
| Mar 10, 2021 at 9:21 | comment | added | Rammus | There are some fringe cases here that I can think of quickly. For example, for a fixed $\rho_A$, if we have that its support is entirely contained within an eigenspace of a unitary operator $U_A$ with eigenvalue $1$ then $U_A$ will have a trivial action on it. For example $\sigma_z |0\rangle = |0\rangle$ but $\sigma_z \neq I$. | |
| Mar 10, 2021 at 7:54 | history | asked | JRT | CC BY-SA 4.0 |