Quantum parameter estimation, Fisher information, and the Cramér-Rao bound
Вставка
- Опубліковано 7 лют 2017
- In this video I give a short introduction to quantum parameter estimation and a result known as the Cramér-Rao bound limiting the variance of a locally unbiased estimator in terms of a quantity called the quantum Fisher information.
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
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
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
Dear Marco,
Many thanks for spotting that one!
Best wishes!
Sincerely,
Tobias
Can you please make videos for am advanced course on Quantum Information
Many thanks for the nice lecture... Any resources on the properties of QFI would be very helpful too.
I like the paper
iopscience.iop.org/article/10.1088/1751-8113/47/42/424006/meta
I hope this helps
Sincerely,
Tobias Osborne
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.
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
@@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.
Is it possible to calculate a Cramer-Rao bound for a neural net?
This seems like an interesting research question: I don't know of any such results. Sincerely,Tobias Osborne
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.
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
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)
Many thanks for your comment!
Indeed, that is absolutely correct, I am assuming that L is then hermitian.
SIncerely,
Tobias Osborne
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
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.
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
Brazilian would pronounce at Kramer wrong