Timeline for Trace of density matrix square greater than 1?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 14, 2022 at 16:41 | vote | accept | peter mafai | ||
| Sep 29, 2022 at 13:11 | answer | added | peter mafai | timeline score: 0 | |
| Sep 29, 2022 at 7:37 | history | edited | Tobias Fünke | CC BY-SA 4.0 |
edited tags
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| Sep 28, 2022 at 22:01 | comment | added | Tobias Fünke | Note that $\rho_{12}\,\rho_{21}=|\rho_{12}|^2 \leq \rho_{11} \,\rho_{22}$, cf. here, and thus, regarding your $2\times 2$ example (where I assume you mean an ONB here): $\mathrm{Tr}\rho^2 \leq \rho_{11}^2 +2\rho_{11}\,\rho_{22}+\rho_{22}^2=(\rho_{11}+\rho_{22})^2 = (\mathrm{Tr}\rho)^2=1$. As shown in the linked answer, the equality holds if and only if $\rho$ is pure. | |
| Sep 28, 2022 at 21:39 | answer | added | hft | timeline score: 2 | |
| Sep 28, 2022 at 21:26 | history | edited | peter mafai | CC BY-SA 4.0 |
expand question with an example
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| Sep 28, 2022 at 10:27 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
edited tags; edited title
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| S Sep 28, 2022 at 10:26 | history | suggested | lcv | CC BY-SA 4.0 |
Fixed title and a few typesetting errors
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| Sep 28, 2022 at 9:23 | review | Suggested edits | |||
| S Sep 28, 2022 at 10:26 | |||||
| Sep 28, 2022 at 9:18 | answer | added | lcv | timeline score: 5 | |
| Sep 28, 2022 at 8:59 | comment | added | flippiefanus | It is a simple property of any set of positive values that add up to one that their squares would add up to a value smaller than one. | |
| Sep 28, 2022 at 8:53 | history | edited | peter mafai | CC BY-SA 4.0 |
added 6 characters in body
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| Sep 28, 2022 at 8:45 | comment | added | flippiefanus | No, you should have learned that tr$\{\rho\}=1$ for all states due to normalization. For pure states tr$\{\rho^2\}=1$ and for mixed states tr$\{\rho^2\}<1$. The situation tr$\{\rho^2\}>1$ is then not possible. | |
| Sep 28, 2022 at 7:48 | history | asked | peter mafai | CC BY-SA 4.0 |