Quantum parameter estimation, Fisher information, and the Cramér-Rao bound

[@marcopiani4885]

Hi Tobias, thanks for sharing this lecture (as well as the other ones)! Just mentioning a small typo in the expression for the Fisher information (the "explicit" one), in case it is useful for others: it is the modulus square of $X_{jk}$ that enters the expression, not the simple square. Cheers, Marco

[@tobiasjosborne]

Dear Marco, Many thanks for spotting that one! Best wishes! Sincerely, Tobias

[@tusharrable]

Can you please make videos for am advanced course on Quantum Information

[@geetrakala8716]

Many thanks for the nice lecture... Any resources on the properties of QFI would be very helpful too.

[@tobiasjosborne]

I like the paper iopscience.iop.org/article/10.1088/1751-8113/47/42/424006/meta I hope this helps Sincerely, Tobias Osborne

[@jungyunhan1097]

Thanks for your excellent lecture! I have subscribed your ''open quantum system lecture" also. By the way, Is this lecture one of the regular class in your school? Or just kind of special lecture? Sincerely, Robert

[@tobiasjosborne]

Dear Robert, Many thanks for your comment! This was a one-off lecture which I presented to give members of our group a foundation to understand current research on quantum Fisher information. Sincerely, Tobias

[@stinkymcstinkington211]

Is it possible to calculate a Cramer-Rao bound for a neural net?

[@tobiasjosborne]

This seems like an interesting research question: I don't know of any such results. Sincerely,Tobias Osborne

[@swayangprabhashaw3009]

Hello sir,thank you for creating this video. It was helpful in understanding QCRB.Sir, can you please share the link of the paper? It would be really helpful.

[@tobiasjosborne]

Many thanks for your comment. The paper in question is: arxiv.org/abs/1008.2417 Look at section 1. I hope this helps; sincerely, Tobias Osborne

[@worththekeeping]

After watching this video and then going to the paper itself, I am very confused why you introduced the superoperator. In the paper, the proof is nearly trivial because you construct the inner product and then immediately apply C-S inequality. My question would be: why did you introduce the super-operator if it is not necessary? Thank you nonetheless for uploading this because before I watched it I struggled understanding Helstrom's 1967 proof of the QCRB.

[@tobiasjosborne]

Thankyou for your message. The basic answer is that I just like the superoperators: you can use them to devise other interesting quantities related to quantum Fisher information. I hope that helps. Sincerely, Tobias Osborne

[@worththekeeping]

@@tobiasjosborne Thanks for your response. As of right now I am failing to see how the review article provides a valid definition of quantum fisher information. Helstrom's 1967 proof provides a different definition of it, but I am sure with more work I can see the connections.

[@bbnCRLB]

You didn't give them the steps by which you arrived at the Fisher Information. This is important as I believe for likelihood with non-zero mean, the Fisher information will contain a second term in addition to the Trace operation you have written. And what if your Fisher Information isn't full rank, i.e. singular in another words. Then you can't invert to have your CRB.

[@tobiasjosborne]

This video is not intended to be comprehensive, and only an invitation. I am happy to recommend arXiv:1008.2417 for further details. Sincerely, Tobias Osborne

[@tanmoybiswas5333]

In general, L is not Hermitian Operator. But If we assume rho(theta)=U rho(0)U^\dagger... Then it will be Hermitian. You have written the F(rho(theta),A) after this assumption.. Right ?? at time (20:10)

[@tobiasjosborne]

Many thanks for your comment! Indeed, that is absolutely correct, I am assuming that L is then hermitian. SIncerely, Tobias Osborne

[@tanmoybiswas5333]

Thanks for the reply. My question was "Is the Hermiticity of L follows from the assumption rho(theta)=U rho(0)U^\dagger" ?? Secondly How you are claiming Omega_rho(theta) is an invertible map? Sincerely Tanmoy

[@michaelmoore7568]

Brazilian would pronounce at Kramer wrong