and that was an active team they built and the team worked well.

Great. So like previous, I want to just thank all the organizers.

I think it's great that they made the effort to have a school like this on the topic of auto mechanics.

Great for the students, great for the community.

I have four lectures here and I think the topic I was asked to speak about was quantum measurements and quantum auto mechanics.

And that's a huge, huge topic. There are lots of things I have to cover.

I'm obviously not going to talk about everything I can possibly talk about.

Focus on sort of issues that hopefully are of interest to you and things that I've been interested in over the last, I don't know, seven, eight years.

I've been working in the mathematics.

So in terms of my lectures, I'm going to start by, I think because I guess maybe I'm the first theorist to really talk,

start by doing something that is hopefully very simple and, you know, friendly.

Just go through the basic theory of quantum capital

But lots of you that will be review.

For others, it will just make sure that you're able to follow the rest of the lectures, both my lectures and the other lectures in this course.

So I'm going to start by, I think because I guess maybe I'm the first theorist to really talk,

start by doing something that is hopefully very simple and, you know, friendly.

Just go through the basic theory of quantum capital in mathematics.

But lots of you that will be review.

For others, it will just make sure that you're able to follow the rest of the lectures,

both my lectures and the other lectures in this course.

And in terms of getting to the meat of my lectures, what I want to talk to you about,

I really want to tell you a lot about trying to understand and properly define the quantum limit on continuous position detection.

And I'm going to tell you more than you ever wanted to know about this subject.

You do a really very general way of understanding quantum limits on measurements in terms of quantum linear response

and the way we should think about quantum limits.

So it's a very very general theory I'll introduce you to.

One that could really work for any kind of quantum linear detector,

but one that works really really well for the kind of cabinet detector we use in optical mechanics.

Okay, from that I will go on to talk about back action.

So how do we make measurements of mechanical positions that are not limited by the back action of the measurements?

And that will be an excuse to introduce you to something else that's sort of interesting from a theory point of view,

the idea of conditional evolution.

So in a particular one of the experiments, I see some noisy outputs in my measurement record.

In that one of the experiments, what is the actual state of the system?

And so how do I describe that theoretically?

How do I use that information to do some kind of feedback operation?

Okay, so that will be in the back action evasion section.

And then, you know, again I have no idea how long this is all going to take.

If there is still time left, I'm going to touch on some topics that are very close to my current research interests.

And this is the idea of coherent feedback or reservoir engineering.

So as opposed to trying to have a system where I make a really good measurement of what my mechanical resonator is doing,

use that to derive some feedback force, put the mechanics in some nice state,

can I design a system that just does that on its own?

It automatically does the measurement and the feedback.

And so that's this idea of coherent feedback or reservoir engineering.

One application of that is this idea of dissipative squeezing.

So a really powerful way to squeeze the state, quantum squeeze the state of the mechanical resonator.

And that's recently been implemented in experiments.

Okay, so kind of long list of things. We'll see how far we get.

I'll always try to get my lectures up on the website in advance of what I give them, so you'll have some notes for follow-up.