# A Quantum Optics statistics

#### winstonboy

Summary
Characteristic Functions in Quantum Optics for linear amplifiers/attenuators
Hi everyone,
I am following along with the MIT OCW quantum optical communication course. I have a question about this chapter, concerning the linear attenuators and amplifiers.

Specifically, the chapter mentions that they are not going to get $\rho_{out}$, but I am interested in this.

More specifically, I am curious about the number of photons detected from the output <n|$\rho_{out}$|n>, which I know will be a function of the arbitrary input state <n|$\rho_{in}$|n>.

I am at the point where I have the antinormal characteristic function $\chi_{out}(\eta,$ $\eta^*)=\chi_{in}(\eta \sqrt{G}$, $\eta^*\sqrt{G})$ for an arbitrary gain $G>1$. How do I proceed from here to get <n|$\rho_{out}$|n>? Do I just take the operator-valued inverse fourier transform, as suggested earlier in the course? If so, I don't know how to do this, so if someone could provide some help in this calculation for a non-coherent state I would appreciate it.

Cheers,
W

Related Quantum Physics News on Phys.org

"Quantum Optics statistics"

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving