Theory of quantum noise and decoherence, Lecture 2

Here in lecture 2 I cover the description of dynamics, both closed and open, in quantum mechanics.

[ANSIcode]

I was hoping this lecture would explain in detail WHY the observable algebra of a composite system is the tensor product of the individual algebras. A lot of controversy seems to be around in various sources as to "how obvious this is"; this includes arguments ranging from "If system A has n possible states and system B has m states, then the system AB will have n*m possible states, tensor product obvious" to "it's a fundamental postulate dividing classical and quantum logic". I'm confused by this. In particular I can't find a detailed discussion of the basic concept of "subsystem" and what exactly that is supposed to be at an elementary level.

[franciscofigueiredo]

Dear Tobias,

The formula you gave for the reduced density matrix involves the following objects:
I_A \tensor <j_A| and I_A \tensor |j_A>|. I'm a bit confused with the definition of these entities. What does it mean to take the tensor product of an operator and a bra (or a ket)?

Thanks a lot for the lectures. They are being very helpful in my studies.

[karabomothupi]

Hey Tobias. Does this course solve the measurement problem? I have been told that decoherence solves the measurement problem.

[marcuspereira]

Hello Dr. Osborne,
Thanks for these great lectures. I don't fully understand from your example of correlated state - p*|00> + (1-p) * |11>, as to why this is not necessarily entangled? It clearly is written as a Schmidt decomposition with more than one term. Therefore, as per definition of entanglement, it should be entangled. Maybe I am missing something obvious. Please help. Thank you!

[amiltonmoreira]

We would be nice if you put references for each lecture

[王博-mr]

Dear professor, are there any English subtitles in your video? I am very interested in your course, but as a foreigner, my listening is very poor. I hope to find some subtitles that can help people in other countries to learn.

[levaniiashvili]

It would be nice if you could give some references for infinite dimentional hilbert space techniques in quantum mechanics and field theory. maybe some papers and books as well (as mathematically rigorous as possible) . thank you in advanced :)