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No doubt that the Schroedinger equation describes the evolution of the wavefunction, hence of its 2^N amplitudes. The problem is that in reality the Hamiltonian, and hence the evolution of the quantum amplitudes, can never be exactly what you would like it to be: H=H_0 +V. Also, the initial conditio

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The wavevector is determined exactly as the solution to the equation
$$ \frac{d}{dt}|\psi(t)\rangle = -iH(t) |\psi(t)\rangle.$$
While the state has $2^n$ dimensions, those do not show up as experimentalist-tunable parameters in this equation. How many tunable parameters are there? Well, those s

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"The only place where 2^N parameters appear is in the wavefunction, not in the Hamiltonian or Lagrangian".

- Certainly. As explicitly stated, I am talking about the wavefunction, which describes the **state** of the quantum system at a given time. You seem to agree that this state is generally d

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This argument lacks detail so it is hard to clearly refute, however one point is clearly wrong. A quantum computer, or quantum mechanics experiment, with $N$ qubits can be described by $O(N)$ or at most $O(N^2)$ parameters. This is because physical Hamiltonians are usually described by 2-body inter

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Dear Blake,

The packing (i.e. the title) is catchy and eye-candy indeed and you are right to accuse the autors of over-selling the content.
At the same time, to be fair, we need to acknowledge their reservation: ,,accepting the photons’ status as observers'' is condicio sine qua non for the resu

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I don't think one can call an experiment an implementation of the Wigner's friend scenario if it's an experiment on photons. The essence of the thought-experiment is that quantum weirdness should apply to a sufficiently careful preparation of *an entire living, thinking observer.* If the "friends" a

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This paper draws a connection between "antidistinguishability" and Symmetric Informationally Complete measurements. One example of such a connection was already known, and it's a bit of a funny story. If you go back to Caves, Fuchs and Schack's "Conditions for compatibility of quantum state assignme

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Yes, I was aware of Rovelli's paper and my aim was to be loosely consistent with it, although the papers differ in that he is concerned with the entropic arrow of time, whereas I am mainly concerned with the causal arrow. It is a deep question what the connection is between the two, though the sugge

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Yes, well spotted! I made an error of omission in the definition of `layered'. It should include the proviso that "every path from an ancestor of X to a descendant of X is intercepted by a node in the layer containing X". That is what I meant, and it is assumed in order to carry out the proofs in th

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We welcome any and all citation requests, even those having to do with pop culture. Thanks for sharing :)

"Thauma" is Greek for "wonder or marvel":

https://en.wiktionary.org/wiki/%CE%B8%CE%B1%CF%8D%CE%BC%CE%B1

which preceded Pratchett by several millennia :)

We indicated this Greek origi

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Love the idea! I'm surprised to see no citation of Terry Pratchett, though. https://wiki.lspace.org/mediawiki/Thaum

Makes sense. Thank you Wojciech.

Dear Marcel,

This condition is just for the ,,All'' face of their Janus-like theorem, and would $ \Omega $ be indeed inaccessible, we would experience just the ,,Nothing''-face.

That is how I understand that.

BR,
Wojciech

I struggle a bit with section 3.4:
"... if the experimenters are given access to an incompressible number (such as Ω) ...".

Isn't the point that exactly this is not possible, because numbers like Ω are not computable?

Hi Tomoyuki,

Thank you for bringing your work to our attention. This paper is a follow-up to [arXiv:1804.10368v2][1], which were together submitted to a journal in December. We will be happy to cite your concurrent work, and are excited to hear that other people are thinking along the same line

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The result in Theorem 1 of this paper was already shown in Theorem 6 of our paper
https://arxiv.org/pdf/1901.01637.pdf

You're right, Aaronson's result applies to integer matrices. I should have linked to [Valiant's original paper][1] which provides a reduction between the case of integer matrices and 0-1 matrices.

[1]: https://doi.org/10.1016/0304-3975%2879%2990044-6

While it is #P hard to compute the permanent of 0-1 matrices, the paper you linked doesn't show this fact. The linear optical proof of Aaronson applies to matrices with entries complicated enough that they can represent universal quantum computation when taken as the beam-splitting unit in a linear

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Doesn't this contradict the fact [computing the permanent is #P-hard][1]? In particular, it is also NP-hard, so it should not have a polynomial-time algorithm.

[1]: https://doi.org/10.1098/rspa.2011.0232

Casual readers of this article, especially those in the target audience of students with an engineering background, might be misled by the way that the term "defect" is being used here in the title and abstract. In an engineering or manufacturing context, a defect is an imperfection that is to be av

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Your work - being a very nice technical result in the framework of causal modeling - has also a familiar ring to the ideas of Carlo Rovelli on [perspectival time's arrow][1].
A little different genres but the same main theme: the asymmetries of time are *produced* by the observer, rather than being

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"Result 1" of this article is "Tomography...is possible...if and only if G is a *layered* DAG.
Nikolov and Tarassov [Discrete Applied Mathematics 154 (2006) 848-860] state (in their first paragraph) that *any* DAG can be layered.

A big hit from 1997 ([https://doi.org/10.1038/37539][1]) with more than 5000 citations. Great to see it also on arXiv.

[1]: https://doi.org/10.1038/37539

Thank you for your comment.

One conclusion which can be drawn from our work, and which is also found in other work such as the one you reference, is of the “overcompleteness” of the axioms of quantum theory. By this I mean that one can remove one of the axioms of the theory and then recover it fr

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Thanks for the interesting idea! One quick question is what the results of two same experiments that start and end at the same time? Will these results be exactly the same?

We studied this type of diffusion-parameter-estimation problem in

(1) Shilin Ng, Shan Zheng Ang, Trevor A. Wheatley, Hidehiro Yonezawa, Akira Furusawa, Elanor H. Huntington, and Mankei Tsang, "Spectrum analysis with quantum dynamical systems," Physical Review A 93, 042121 (2016); http://dx.doi.org/

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Very interesting. I should read your paper more carefully, but it sounds like this (pretty old) paper by Vladimir Buzek, Nicolas Gisin and myself (which was based on even older work by Nicolas Gisin) is in some sense complementary: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.170405

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In response to the government shutdown I have put the zoo up at:

http://quantumalgorithmzoo.org/

It remains 6 months out of date, but I hope to update soon....

Note for other scientists like me who would wonder why the quantum algorithm zoo would shut down and when it will be operational again. It is hosted at NIST and is therefore part of the current [US federal government shutdown][1]. I guess your favorite news source will therefore tell you when it wil

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Even better!

> Our interactive labeling and semi-supervised extension of t-SNE is available in the newest version of TensorBoard Projector...

Sounds like it's already integrated in tensor board

Nice; will be good to see code.

Thank you for the interesting references! I will have a look.

Universal quantum computation based on permutations is investigated here
https://arxiv.org/abs/1701.06443
and subsequent papers, may be it connects to your interesting paper.

I don't know of any mirror, but you can use the internet archive for a recent snapshot: https://web.archive.org/web/20181208091423/https://math.nist.gov/quantum/zoo

The quantum algorithm zoo (http://math.nist.gov/quantum/zoo/) mentioned in this paper appears to be currently shut down?! Is there any alternative way to the zoo? Thank you.

http://www.mathnet.ru/php/seminars.phtml?option_lang=rus&presentid=9249

This includes an erratum for the 2013 *Reviews of Modern Physics* article by Fuchs and Schack (arXiv:1301.3274).

I suspect that the conjectures vary in difficulty, though of course I can't say this for sure until they've been proven. Some of them might be "textbook exercises of the future", in th

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Is this a research note? The definitions for symbols are sometimes missing.

In Appendix B there is a fragment:

> Consider a set of balls bouncing on
a billiard table [...] A moment of reflection
shows that entropy, so defined, generically increases from
$ t_a $ to $ t_b $ if it is defined by $ O_a $, but decreases if it is defined
by $ O_b $.

I think that much cl

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Thank you for drawing my attention to this paper.

Having read through the paper I would say it is related to the work we reference and we will cite it in the next version of our manuscript. There are however a few differences.

Cabello's paper singles out the set of quantum correlations from the

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One small comment of a layman, you write:

> The Born rule has been derived within the framework of quantum logic, taking an operational approach, and using other methods. But all these derivations assume, among other things, the mathematical structure of quantum measurements, that is, the corresp

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Anyhow, wouldn't be any theory or interpretation useless, ridiculous as a worldview, were such a basic assumption invalid?

Thank you for your comment.

Yes, I agree that there is a prima facie incompatibility between the assumption that measurements have definite outcomes and the many worlds approach. Indeed I think that more generally there is a certain incompatibility between the operational approach to physical theor

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It is not clear that this result would apply to the many-worlds interpretation. The authors state their assumption "that there exist experiments which yield definite outcomes (possibly relative to a given agent who uses this formalism), and that it makes sense to assign probabilities to those outco

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Hi Ashley.

"Is there another ensemble of random graphs which would be a better test case, in the sense that the best known classical algorithms do badly (empirically or theoretically) at approximating the max-cut?"
-- I assume you're imagining cases that are not derived from NP-hardness? (I'm

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Is there another ensemble of random graphs which would be a better test case, in the sense that the best known classical algorithms do badly (empirically or theoretically) at approximating the max-cut?

"I don't think we will see QAOA for n = 10000." ... only if we never have a quantum computer wi

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I must admit that I don't see why this paper is convincing. The question is: Why did the author compare against the Goemans--Williamson algorithm (especially given that the test graphs were random G(n,1/2) graphs)?

1. It is well known that Goemans--Williamson performs poorly when the max-cut (no

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I like Sandu's provocation, but I don't think we need a new type of quantum state. We should not just consider Alice's description of the state and her memory, but should write a three party density matrix (Alice, Charlie, Spin). The tripartite density matrix is adequate for describing all experimen

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These are precisely the kind of classical-quantum states everyone uses in quantum Shannon theory and they are equivalent to hybrid density operators.