Timeline for Geometric interpretation for partial trace?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| May 29, 2021 at 23:53 | answer | added | Joseph Van Name | timeline score: 1 | |
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 23, 2015 at 23:49 | comment | added | Suvrit | In other words, if $A=X \otimes Y$ is tensor product of density matrices, then $\text{tr}_2(A)=X$ and $\text{tr}_1(A)=Y$ (this is the marginalizing out that Carlo mentioned). | |
| Mar 23, 2015 at 13:26 | comment | added | Igor Khavkine | Partially dualized, $f\in \mathrm{Hom}(X,Y)\otimes (U\otimes U^*)$. Partial trace is then the linear map $\mathrm{Hom}(X,Y) \otimes (U\otimes U^*) \to \mathrm{Hom}(X,Y)$ given by $\mathrm{id} \otimes \delta$, where $\delta \in U^*\otimes U \cong (U\otimes U^*)^*$ is the dualized version of the identity map $U\to U$. I don't know if this is very geometric, but it's certainly an invariant description of the operation. | |
| Mar 23, 2015 at 7:13 | comment | added | Carlo Beenakker | a physics interpretation is that the partial trace is the way one obtains marginal probability distributions in quantum mechanics: the density matrix $\rho$ describes the probability distribution $P_{X,U}$ of the combined systems $X$ and $U$ and by performing the partial trace over $U$ one obtains a new density matrix $\rho_X$ that describes the marginal distribution $P_X$ of system $X$ alone; this is not the geometric interpretation you are asking for, but I would think that if you have a "geometric interpretation" of the marginal distribution then you're done. | |
| Mar 23, 2015 at 3:06 | history | asked | David Spivak | CC BY-SA 3.0 |