Timeline for Partial trace over a product of matrices - prove that ${\rm Tr}(\rho^{AB}(\sigma^A\otimes I))={\rm Tr}(\rho^A\sigma^A)$
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 14:06 | comment | added | John Watrous | No, I mean that the span is the entire space, even if $\rho_A$ and $\rho_B$ range over all positive semidefinite, trace-one matrices. | |
| Jun 15, 2020 at 3:31 | comment | added | user1936752 | Just to clarify, when you say that "the set of all product states $\rho_A\otimes\rho_B$ spans $H_A\otimes H_B$", do you mean that the $\rho_A$ and $\rho_B$ here are arbitrary matrices? We cannot restrict them to those with unit trace or to be positive semidefinite, correct? | |
| Jun 21, 2019 at 12:48 | comment | added | John Watrous | No, it holds for all $X$, $Y$, and $Z$. | |
| Jun 21, 2019 at 4:54 | comment | added | Mahathi Vempati | Tr((𝑋⊗𝑌)(𝑍⊗𝐼)) =T r(𝑋𝑍)Tr(𝑌) = Tr(Tr𝐵(𝑋⊗𝑌)𝑍). This statement does not hold true irrespective of traces, right? In particular, the Trace of Y has to be 1 for this to hold true? | |
| Jan 2, 2019 at 11:19 | vote | accept | Mahathi Vempati | ||
| Dec 28, 2018 at 13:36 | history | answered | John Watrous | CC BY-SA 4.0 |