Is it actually decidable? :-)
I like this sentence from the conclusion: "There is, however, a second possible answer to our question: yes".
Here is a link for those who also haven't heard of SciPost before: https://scipost.org/
This is the very first paper of SciPost, waiting for the first paper of "Quantum" (http://quantum-journal.org). There are radical (and good!) changes going on in scientific publishing.
"Ni." would be slightly shorter, but some may find it offensive.
The abstract my be a bit too long.
I would suggest planets where life can really make a difference.
I am still trying to understand the following statement from II.A.
> This leads to the condition that the first- and second-order moments
> of the model and data distributions should be equal for the parameters
> to be optimal.
John also has an excellent series of 7 blog posts covering this material:
https://www.physicsforums.com/insights/struggles-continuum-part-1/
...(continued)I think that we have missed the "semi-" at the conclusion. Because, the proof of the theorem 4.3 is based on the using universal semi-density matrix concept which is not computable. The semi-computability concept used here is like the Kolmogorov complexity which is not computable and so the Cubic co
...(continued)I could well be missing something. But as far as I could tell from a rather quick read through the paper, all they show is that the quantum capacity of a channel with computable matrix elements is given by the regularised coherent information optimised over input ensembles with computable matrix ele
Do I understand correctly that this paper claims to show that quantum capacity is computable?
> After defining the algorithmic quantum capacity we have proved that it
> equals the standard one. Furthermore we have shown that it is
> computable.
That is really a long-term perspective.
Born in Italy, and now living in Scotland: I have no excuses not to feel inspired :-)
...(continued)It is not just in Scotland but in fact across the whole of UK and even beyond. I just found a reference, dating back to the very birth of quantum computing, where the early pioneers [already admit][1] that their work was inspired by Rabezzana Grignolino d'Asti.
[1]: https://scirate.com/arxiv/quan
A video of a talk I gave this morning will be [here][1], if it ever finishes uploading.
[1]: https://youtu.be/I8cMY0AmIY0
...(continued)Hi, sorry to just be updating this discussion now -- my conversation with Renato seemed to me to have converged here (and also continued via email and in person and I never updated scirate). However, a few people have asked what the outcome of our discussion was. So let me just say, that yes, my vie
Conjugate Gradient IS a Krylov-space method...
...(continued)I completely agree with your analysis, which describes the gedankenexperiment from a global (“outside”) perspective, according to the laws of Bohmian Mechanics (BM). And, indeed, it shows that the "memory" of a measurement outcome cannot assumed to be permanent, i.e., it may change (according to BM)
...(continued)Roger Colbeck drew our attention to this paper in the York QFIT group, and we met to discuss it last week. I would like to comment on the relation of Bohmian quantum mechanics to the extended Wigner's friend experiment. As generalised by John Bell, Bohmian qm can be applied to this experiment to yie
...(continued)Video of a *journal club* session about this paper, with a 20min explanation of the paradox and a long audience discussion about implications and interpretations:
http://pirsa.org/16060101/
Notation: "for simplicity" some names have been revealed (like the friends'), some have been changed
Too bad, the paper has been withdrawn due to a mistake :-/
...(continued)Maybe. But if your solution was not only self-consistent but also "single-world" then it would certainly contradict our theorem.
@Jonathan: I am unsure whether the concern you had is related to ($\star$), too, but I would anyway be interested to know whether it is this type of statements that you
If I had a self-consistent answer to that I'd be able to solve the measurement problem, no?
...(continued)OK, then we have identified the point where we disagree. Our assumption (QT) indeed corresponds to ($\star$), together with the understanding that the state is physically relevant.
Having said this, I am still curious to know how, in your opinion, experimenter F1 should derive her prediction ab
Yes, I would say so.
Could one then summarise your viewpoint as follows: Statement ($\star$) by itself is correct, but the state $\psi$ of the system is not the one that is physically relevant (i.e., we should not use it to deduce claims about the outcomes of future measurement on the system, for instance)?
...(continued)I think our point of disagreement is not $(\star)$ in itself, but rather the relevance of $\psi$ that enters this statement. I would also make the second bullet point stronger.
- When discussing erasure and subsequent measurements, one needs to keep track of both $E$ and $S$, even if they are no
...(continued)Yes, it may be easier to chat about this in person. But since I know a few who are following this discussion, let me at least summarise the points where I agree with you:
- In a scenario where experimenters are themselves subject to quantum measurements, it is not allowed to describe them using c
...(continued)The point I was originally trying to make was that the experimenter must be treated within the same framework as the system. The argument I was trying to make was that it is not always justified to treat the experimenter as classical (what I said above regarding the environment can be rephrased to t
...(continued)The example itself makes sense to me. However, I am unsure how it connects to the questions we were discussing.
Certainly, it illustrates that the statement ($\star$) mentioned earlier would be wrong if there was a non-trivial exchange Hamiltonian governing the interaction between experimenter a
...(continued)In a sense, yes, that's what I'm saying.
Let me take a situation that is very familiar to me: Cavity QED. We model a single-mode field inside a cavity with leaky mirrors by means of an interaction Hamiltonian like $\hat{H}_\text{int}=\mathrm{i}\hbar\int\mathrm{d}\omega\ \kappa(\omega)\bigl[\hat{b}(
...(continued)Just to make sure I got this correctly, are you saying that (at least in certain situations) the predictions we obtain when we use quantum theory depend on where we make the split between quantum system and measurement device? (This would raise the question whether there is a rule that tells us wher
...(continued)I won't attempt to solve the general problem. At least not without some beers.
My point was directed at the particular argument at hand.
- I have a laboratory $L$ inside which is a quantum system $S$ and an experimenter $E$
- $E$ performs some measurements on $S$, but $E$ is not treated as part
...(continued)I agree with what you wrote in the last paragraph — you may even regard this as an implication of our Theorem 1 (at least provided that you take SW for granted).
I nevertheless have difficulties making full sense of the position you take. If I understand it rightly, the ultimate conclusion would
...(continued)The ability to impose a "cut" and isolate a system (e.g., a single H atom) from its surroundings and treating that system as a quantum object disconnected from its surroundings, or connected to them solely by means of classical channels, is an extremely convenient fiction. But it is, at the end of t
...(continued)My previous statement must have been ambiguous. But when I wrote that an experimenter applies quantum theory to a system, I did not mean to imply that she applies classical theory to its surroundings. Rather, the idea was that she can use QT to study any arbitrary subsystem of the universe, provided
...(continued)My understanding of quantum theory is precisely that: It must be applied to the experimenter themselves as well as the apparatus. I come from the school of thought that believes that everything is quantum.
As per my previous comment, within this framework it may be possible that your paper could
Indeed, our argument is based on the idea that any experimenter is free to use quantum theory to describe the world *around* her (but not including herself). If I now understand correctly, you are saying that this is not in general a correct use of quantum theory. Did I get this correctly?
I don't think that QIC is to blame here. ECCC is also not indexed by google scholar for some strange reason. Try this paper http://eccc.hpi-web.de/report/2016/073/ for instance.
...(continued)You are perfectly right; that is exactly what confused me.
Personally, then, I feel slightly uneasy with saying that your property QT captures quantum mechanics, since I believe strongly that quantum mechanics must describe the state of the experimenter themselves. This is especially pertinent in
...(continued)I agree with what you are writing about $\psi_L$. While the state of the prepared system $S$ does not depend on whether $E$ remembers it, the state $\psi_L$ (which includes $E$) does.
I am not sure though what you meant when you wrote that $\psi_L$ is the "relevant object". Note that property QT
...(continued)Actually, the Bayesian perspective did not enter my mind.
I *almost* agree with the reformulation you give in your second paragraph. I say "almost" because of one detail that I feel is important in the context of your paper, and which for me is the key issue at stake here.
Suppose I have a lab
...(continued)I am not sure why you think that the state $\psi$ must change. But one guess I have (please correct me if I am wrong) is that you take a Bayesian perspective, in which case there may be an ambiguity in the interpretation of time t. So, maybe, you interpreted t as the time when the prediction was mad
...(continued)This paper somehow got published in QIC. Not that I would encourage anyone to read it, but let's say you wanted to...
Well, you would probably just [look up][4] the published version on Google Scholar.
What a bummer(!), it's not there... Maybe that's just because the paper's name has changed?
...(continued)Dear Renato, may I also join the chorus and thank you for being so accessible and willing to discuss your results publicly. I've been following this thread since its inception but have so far resisted contributing.
Please correct me if I am wrong, but does not a full description of $\psi$ require
...(continued)looks like a nice paper. People have looked at how to do wavelets with quantum circuits and i don't see any of these papers referenced, i.e.
http://arxiv.org/abs/quant-ph/9702028
http://arxiv.org/abs/quant-ph/0001077
http://arxiv.org/abs/quant-ph/9909014
so how different are the quantum circuits
...(continued)Practicalities are indeed irrelevant here, so we can certainly focus on the last question you pose. But let me first restate more precisely what we use in our argument. In the special case of a system with trivial Hamiltonian between time t=0 and t=1, the relevant statement reads as follows: “If an
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