Timeline for Regarding density matrix eigenvalues
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 14, 2020 at 15:23 | comment | added | ZeroTheHero | @MarkMitchison Good point. I know that but somehow overlooked this in crafting my answer as I was focused more on the "complex eigenvalue" part of the question. Thanks for bringing it up. | |
| May 14, 2020 at 14:50 | comment | added | Mark Mitchison | Apologies for nitpicking but positivity (as well as hermiticity) does place constraints on the off-diagonal elements as well as the diagonal ones, e.g. in dimension 2 one requires $|\rho_{12}|^2 \leq \rho_{11}\rho_{22}$ so that $\det \rho \geq 0$. | |
| Apr 23, 2020 at 10:05 | vote | accept | self.grassmanian | ||
| Apr 23, 2020 at 8:40 | comment | added | ZeroTheHero | not really helpful. The trace is invariant under conjugation so all it says it that your initial $\rho$ has trace=1. Check hermiticity. | |
| Apr 23, 2020 at 7:51 | comment | added | self.grassmanian | I have checked that Tr$(\rho) = 1$, can that somehow help? | |
| Apr 22, 2020 at 20:40 | comment | added | ZeroTheHero | Of course not. The hermiticity condition remains even for composite systems. There is no way your $\rho$ is hermitian if you have complex eigenvalues. | |
| Apr 22, 2020 at 20:33 | comment | added | self.grassmanian | Actually, I am working on something an having a $\rho_{4\times4}$ with complex eigenvalues. Is it possible to have such for the case when we have mixed states or entanglement? | |
| Apr 22, 2020 at 20:30 | history | edited | ZeroTheHero | CC BY-SA 4.0 |
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| Apr 22, 2020 at 19:58 | history | edited | ZeroTheHero | CC BY-SA 4.0 |
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| Apr 22, 2020 at 19:53 | history | answered | ZeroTheHero | CC BY-SA 4.0 |