Timeline for Composing beam splitters
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 21, 2023 at 13:32 | history | edited | Quantum Mechanic | CC BY-SA 4.0 |
changed notation of eta matrix from theta to eta
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| Dec 21, 2023 at 13:31 | comment | added | Quantum Mechanic | @Quantastic the boldface was just for emphasis, not to mean anything about notation. The part in bold is the part you can use input-output theory to calculate and will turn into a linear combination of operators of the form $a^\dagger b$, etc | |
| Dec 21, 2023 at 11:26 | comment | added | Quantastic | alright, this makes sense! Just out of curiosity, did you mean to type that part of the last equation in boldface? | |
| Dec 20, 2023 at 14:37 | comment | added | Quantum Mechanic | @Quantastic you can just do $UV=UVU^\dagger U$ and use BCH to find $UVU^\dagger$. It won't be very nice though. There is nothing wrong with leaving the channel as $UV$ - that might be the easiest form! Then if you want derivatives for QFI or something, it's just $\partial U_\theta V_\eta /\partial \eta=U_\theta \partial V_\eta/\partial \eta$, etc, for which you just need this input-output theory to find $\partial U_\theta V_\eta /\partial \eta=U_\theta (a^\dagger c+a c^\dagger)i V_\eta=\boldsymbol{U_\theta (a^\dagger c+a c^\dagger)U_\theta^\dagger} \times i U_\theta V_\eta$ | |
| Dec 20, 2023 at 1:45 | comment | added | Quantastic | I guess the point is that I am more interested in the channel itself than its application to any specific state (for example, to calculate things such as its distance to other channels, the QFI, etc.). | |
| Dec 19, 2023 at 23:14 | comment | added | Quantastic | Thank you for your answer, it is definitely useful. However, you touch on the thing that interests me the most only in your last paragraph: how do you write $U$ using the BCH formula? Do you just the approximation $e^Ae^B\cong e^{A+B+\frac12[A,B]}$? | |
| Dec 19, 2023 at 21:01 | history | answered | Quantum Mechanic | CC BY-SA 4.0 |