Recent content by Ameno

Thanks, this makes sense. Am I right to say that T^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial^\nu \phi - \delta^{\mu\nu} \mathcal{L} and T^{\mu\nu} = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial^\nu \phi - g^{\mu\nu} \mathcal{L} are the...

Hi This might be a stupid question, so I hope you are patient with me. When I look for the definition of the energy-momentum tensor in terms of the Lagrangian density, I find two different (?) definitions: {T^\mu}_\nu = \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}\partial_\nu...

Well, there are two ways I know how one can do this. One is what you have just written, the other one is to check if there is a unitary matrix s.t. N_a = U_{\mu a}M_\mu where the N's and M's are the operators of two operator-sum representations. I find that both require a lot of time to work...

Hi According to the Kraus representation theorem, a map \mathcal{E}: \text{End}(\mathcal{H}_A) \rightarrow \text{End}(\mathcal{H}_B) is a trace-preserving completely positive map if and only if it can be written in an operator sum representation \mathcal{E}: \rho \mapsto \sum_k A_k \rho...

Yes, but wouldn't this require a choice of representation? It would not require a choice of basis, but it wouldn't be canonical in the sense of independence of representation.

Thanks. OK, I also had this answer in mind (which I already found), but I thought that there is a simpler answer because this statement appeared at a point in the script where that basis has not yet been introduced. Perhaps I'll find a simpler answer, but I'm also fine with this one. At least...

Hi I've just read the statement that a matrix that commutes with all four gamma matrices / Dirac matrices has to be a multiple of the identity. I don't see that; can anyone tell me why this is true? Thanks in advance

Yes, this really helps! This is the kind of explanation I was looking for. It explains how an observer can effectively see an incoherent superposition without talking about wave function collapse. It also explains why quantum erasure is difficult to be produced experimentally: Either one has...

Thank you very much for your answers. Now I think I know what the crux of the matter could be, although there are still things I don't get. Let's discuss point 2 (the measurement with respect to the z-axis) again. The descriptions of the measurement without taking notice of the result that...

Sorry for the late answer, and thank you for your replies which confirm my guess that things are somewhat more subtle than claimed by the above statement. For example, I asked a Ph.D. student who is engaged in quantum electronics about the diode laser that I proposed as a counterexample, and he...

Hi I am currently reading John Preskill's Lecture Notes on Quantum Information and Quantum Computation (see http://www.theory.caltech.edu/people/preskill/ph229/index.html near the bottom of the page). I am confused about what he writes in chapter 2.5.4: Quantum erasure. He starts with the...

Hi I would like to understand the statement that "there cannot be a two-level laser" in a bit more detail. I understand that given an active medium consisting of two-level systems, one cannot pump it using photons with an energy equal to the energy gap to reach population inversion, because...

OK, let's do another attempt to approach your issue. As usual in quantum information theory, we make examples involving two parties, called "Alice" and "Bob". Say that Alice and Bob agree on the following procedure: First, Alice prepares a three-qubit system in some state. Then, she gives...

The state of a qubit is (in the Bloch ball representation) described by a point in a ball (or on a sphere, if one restricts to pure states), so one might hope that one can store an infinite amount of information in a qubit and retrieve it by measurement(s). But this is not the case. The famous...