So "quantum information" is a bit of a pop science buzz word it sounds like. It's unfortunate that I've been trying to puzzle it out then.
However, some good came from this discussion and I think you all for your time. Specifically, the mention of Weyl quantization (by others) and symmetry...
I can't seem to wrap my head around the notion of conservation of quantum information. One thing that might help that is if someone can tell me what the associated symmetry is. For example, phase symmetry leads to conservation of electric charge according to Noether's theorem; a fact that...
I've been studying the Witten-Reshetikhin-Turaev (WRT) invariant of 3-manifolds but have almost zero background in physics. The WRT of a 3-manifold is closely related to the Chern-Simons (CS) invariant via the volume conjecture. My question is, what does the CS invariant of a 3-manifold...
If I understand the theory of quantum invariants of 3-manifolds correctly (possibly I don't), TQFTs on different presentations of closed 3-manifolds produce different values. However, the same quantum invariants (Reshetikhin-Turaev invariants for example) are produced on a closed manifold...
https://www.ma.utexas.edu/users/dafr/OldTQFTLectures.pdf
I'm reading the paper linked above (page 10) and have a simple question about notation and another that's more of a sanity check. Given a space ##Y## and a spacetime ##X## the author talks about the associated Quantum Hilbert Spaces...
That's quite possible. So then, what are characteristic numbers, how are characteristic numbers related to Dijkgraaf-Witten theory and what physical quantity (if any) do they correspond to in the real world?
The only type of characteristic numbers I'm aware of come from representation theory...
I like where your intuition is going with that. Unfortunately I would need to study the theorem of Noether you mention more extensively before even beginning to consider what you suggest. I do understand enough to see why you might suggest that though.
I don't think I articulated my question very well. Let me try again: The number of principal G bundles of a manifold is a topological invariant. What I would like to know is, does that invariant correspond to any physical quantity?
I've been studying TQFT and gauge theory. Dijkgraaf-Witten theory in particular. One learns that a topological field theory applied to a manifold outputs the number of principal G bundles of a manifold.
My question is for the Physicists in the room, why do you want to know the number of...
I worked my way through this paper
http://www.math.harvard.edu/theses/senior/lee/lee.pdf
as part of a mathematics reading project and believe I have a fairly good understanding of the material. There is virtually no physics in this paper yet we seem to arrive at Dijkgraaf-Witten Theory quite...
I keep hearing that QM and GR don't play well together. For example, a singularity, a result of GR, is small enough for QM to apply but...it doesn't. I was hoping someone could explain exactly where the "equations fail." Unfortunately I'm so ignorant in this subject matter that I can't be...
Momentum and position are canonically conjugate in physics because they are the fourier transforms of each other.
In the context of abstract algebra what would that mean. More precisely, Let G be the group they both (p and x) belong to and let ψ:G->G/H be the natural homomorphism where H is...
The Schrodinger equation for the complex conjugate of a ket vector is:
d/dt<sai(t)| = -(<sai(t)|H)/(i*hcross)
How do you derive the above equation from the normal form of the schrodinger equation? I'm mostly confused by where the negative sign is coming from.
Thanks
http://en.wikipedia.org/wiki/Coherent_state#Quantum_mechanical_definition
From the link above:
"Physically, this formula means that a coherent state is left unchanged by the detection (or annihilation) of a particle."
My question is, why is detection of a particle equivalent to...
I'm trying to test my understanding between a mixed state and a pure state.
Suppose you have two electrons in a quantum system. If I want to calculate the expectation value of the operator, A, of the system I have to use a density matrix in the calculation.
Now suppose the two electrons...
OK, I guess I don't know the difference between statistical mixture and superposition of two eigenstates. In fact, I always thought the superposition of two eigenstates where the norm is 1 was a statistical mixture. Thanks though, now I know where the hole in my basic knowledge is and what I...
I pasted a paragraph from http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-845-quantum-complexity-theory-fall-2010/lecture-notes/MIT6_845F10_lec02.pdf" [Broken] below.
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Consider the following matrix which represents a 45◦ counter clock...
OK, I agree. In that case, is there any connection between Lie Algebras and Algebraic Topology? If so, I suppose that would be my next area of interest.
I think I get the difference between spinors and tensors in the context of algebraic topology and QM but I want someone to scrutinize my understanding before I move on to another topic. I've never had a class in topology so I might be using some math terms incorrectly.
The 3D parameterized...
http://www.tampa.phys.ucl.ac.uk/~tania/QM4226/SEC4B.pdf [Broken]
At the above link, I'm not quite sure how the instructor got to the matrix definition for Sn(equation 4.61 on page 4) from n dot s. Does someone know of a link that doesn't skip that step?
OK, so I was intrigued by the name quantum teleportation and wanted to know what it was. So, I study QM and linear algebra for 6 months up to the point where I can understand entaglement very well. Then, I go back to study quantum teleportation with the proper tools. If I understand correctly...
Towards the end of http://www.youtube.com/watch?v=IAgV-LKTiMI&feature=channel" video at 54:55, the professor defines the four possible states of two entagled electrons as follows:
singlet
|0,0> = |u,d> - |d,u>
triplet
|1,1> = |u,u>
|1,0> = |u,d> +...
I'm watching a series of lectures on QM and the last one dealt with entaglement. You can see it http://www.youtube.com/watch?v=IAgV-LKTiMI&feature=channel" if you want. I understand it in the purely theoretical sense. It's a very neat concept.
Naturally, my next question is, how would you...
I watched a lecture that derived the properties of the angular momentum operators J and J3 using two QHOs and a bunch of algebra. The initial assumption was that two independent QHOs somehow correspond to angular momentum and everything was derived from there. I understand all the algebra...