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**The squashed entanglement of a quantum channel**

(http://arxiv.org/abs/1310.0129) by Masahiro Takeoka (1,2), Saikat Guha (2), and Mark M. Wilde (3)

- National Institute of Information and Communications Technology, 4-2-1 Nukuikita, Koganei, Tokyo 184-8795, Japan
- Quantum Information Processing Group, Raytheon BBN Technologies, Cambridge, MA 02138, USA
- Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA

This is one in a long series of papers that lie about the origins of Squashed Entanglement. The paper attributes the invention of squashed entanglement to Christandl and Winter. This is an outright lie, as one can easily establish by consulting arXiv.

As the Wikipedia article on squashed entanglement clearly documents, giving pertinent arXiv references, I had submitted to arXiv about 5 papers on squashed entanglement, giving the EXACT modern definition, and I had even written a C++ computer program to calculate it, about 3 years before Christandl-Winter wrote their first paper on it. (although I didn’t call it squashed entanglement, I just called it a generalization of the definition given by Bennett, et al. of entanglement of formation for mixed states, not a very catchy name I must admit, although I don’t think the name squashed entanglement is much of an improvement). I had also sent email to Winter pointing out my papers to him before he wrote his paper with Christandl about squashed entanglement.

It seems that Masahiro Takeoka, Saikat Guha, Mark M. Wilde are doing this to hurt me because they are dumb, unethical, nasty thugs. They are too dumb to realize that their paper in no way detracts from my work. All their paper does is to hurt their own reputation, by giving tangible evidence that they are dishonest scientists and immoral people. And now that this paper is on arXiv, this evidence will follow them for eternity. The duration of the punishment is extremely harsh, but it’s not my fault. Blame Paul Ginsparg, main arXiv inventor (?), for it 🙂

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Those jerks! They make me so mad. And wouldn’t you know, they acknowledge Seth Lloyd. Evil, rotten people.

Comment by Max Born — October 2, 2013 @ 9:42 pm

“Nuke’m till they glow and shoote’m in the dark!”

Comment by Elagnel Exterminador — October 4, 2013 @ 3:42 pm

El Angel, That video is a pale, derivative work of the much more vivid myth of your Greek compatriots

http://en.wikipedia.org/wiki/Saturn_Devouring_His_Son

Cronus reminds me of a university professor eating PhDs who are not in academia (the vast majority of PhDs)

Comment by rrtucci — October 6, 2013 @ 1:25 pm

Two questions: 1) Why would the authors want to hurt you? You are not saying that they have failed to cite your works, but that they have consciously chosen to do so to hurt you: what is your evidence for such an accusation? 2) How comes many of your papers are not published in peer-reviewed journals? In order to trust the claims in those papers I would have necessarily to check them myself, instead of potentially rely on the quality stamp of the peer-review process.

Comment by anon — October 7, 2013 @ 4:38 pm

1) Read the introduction of their paper. Then look at the arxiv links given in the wikipedia article on squashed entanglement. Make up your own mind. It’s actually funny how they trace the history of squashed entanglement to early Roman times, making sure to brown nose every single past emperor, adulating them for every sneeze they’ve ever made, but they somehow manage to miss my 5 papers.

2) Your question 2 is just a red herring. ” In order to trust the claims in those papers I would have necessarily to check them myself” Yes, that’s what you are supposed to do when you write a paper. And with arxiv it’s just a few clicks away so there is no excuse. Squashed entanglement is a definition, not a theorem, so it hardly needs checking

Even though 2 is a red herring, I’ll answer it. I don’t publish in peer reviewed journals because that costs a lot of money and I can’t afford it (like a lot of people in South America and Africa and Greece, I might add). I do not have government funding. Some journals allow free publication for poor people, but I refuse on principle to accept such handouts.

Comment by rrtucci — October 7, 2013 @ 5:24 pm

http://www.nature.com/news/open-access-the-true-cost-of-science-publishing-1.12676

Comment by mikemcglincy — October 11, 2013 @ 1:15 am

Since my work with coauthors Saikat Guha and Masahiro Takeoka was publicly disgraced without the author of this blog contacting us privately before doing so (as is a common courtesy in the quantum information theory community), I think it is appropriate for us to mention a few clarifying, pertinent points. (I will address only the substantial points made by the blog author, as there are many irrelevant ones present.)

Although it is clear that Tucci defined some interesting functions of quantum states that appear similar to squashed entanglement, it is important to realize that these functions are *not equivalent* to the squashed entanglement. Furthermore, the Wikipedia article on squashed entanglement and this blog post are misleading and contain several inaccuracies (as do the unpublished papers of Tucci).

The insight of Christandl and Winter was to develop the squashed entanglement as a quantum generalization of the intrinsic information, as given by Maurer and Wolf in their original papers. Critical in the definition of the squashed entanglement is an *infimum* over all extensions rho_ABE of the state rho_AB of interest. With this, the squashed entanglement has been established by many authors to satisfy all of the desirable criteria for an entanglement measure (as cited in our paper). In this sense, the squashed entanglement is thus one of the best entanglement measures available.

One of the most important open questions concerning the squashed entanglement is whether it is possible to place an upper bound on the dimension of the extension system, such that it would only be necessary to take an infimum over extensions of a fixed size. If it were possible to do so, then we could safely replace the infimum in the definition with a minimum. The papers of Tucci and the Wikipedia article on squashed entanglement underplay the importance of this issue. It very well could be the case that it might be possible to replace the infimum by a minimum, but until someone resolves this issue, the definition must have an infimum.

In light of these observations, we can now point out some flaws in this blog post:

1) The papers of Tucci do not give the exact modern definition as claimed.

2) As the infimum must be taken over an extension system of unbounded size, it is not even clear whether it is possible to compute the squashed entanglement in non-deterministic polynomial time. Thus, a claim that it is possible to have a C++ computer program for computing it is unsubstantiated.

Similar comments apply to the Wikipedia article on squashed entanglement.

I have communicated with Winter on the claim of emails from Tucci to Christandl and Winter before the publication of their work on squashed entanglement. This claim is false. It was only after Winter and Christandl published their work to the arXiv that Tucci emailed.

It was never our intention to hurt the feelings of Tucci by not citing his work. It was just my feeling at the time of writing up our paper that there was a big gap between what was established in the Christandl-Winter paper and the Tucci papers regarding squashed entanglement, and the seeming unawareness of these critical issues in the Tucci papers and further unsubstantiated claims of being able to compute squashed entanglement in polytime. However, in an update to our paper, we have now included a citation to Tucci’s work and have thanked him for pointing out his work on the topic. Finally, we would like to invite the readers of this blog to read our paper to discover the advances our work has given in understanding a longstanding open question in quantum information theory, namely, the effort to determine better bounds on the quantum capacity of a quantum channel assisted by forward and backward classical communication. The squashed entanglement of a quantum channel allows us to do so.

Comment by Mark M. Wilde — October 17, 2013 @ 3:33 am

“contacting us privately before doing so (as is a common courtesy in the quantum information theory community)”Yours was not a simple oversight. It was a blatant lie meant to hurt my reputation and make me look like fool and a liar. Luckily, arXiv doesn’t lie and everything I’m saying can be checked with just a few clicks.

“The papers of Tucci do not give the exact modern definition as claimed.”Yes it does, The Wikipedia article gives an arxiv reference and exact equation number for those who want to check it. My definition only differs from your brilliant improvement in that I use a “min” instead of an “inf”. It is well known that an inf and a lim inf are simple generalizations of a min. Furthermore, a lot of people, especially physicists like me (also Shannon in his papers and Bennett et al in their definition of entanglement of formation for mixed states) do not distinguish clearly those cases in which their min should be changed to an inf or even a lim inf, even though one can easily cook up examples in which a simple min will not do. Does that mean that you instead of Shannon should be considered the inventor of information theory and you are justified in omitting from your papers all mention of Shannon’s work, because you had the brilliant insight to replace all his mins by infs and maxs with sups. Pretty ridiculous.

“Thus, a claim that it is possible to have a C++ computer program for computing it is unsubstantiated.”I must have imagined that I wrote a computer program and wrote a paper reporting the findings

http://arxiv.org/abs/quant-ph/0101123

(In the abstract of that paper, I refer to squashed entanglement as entanglement of formation because I refer to both the definition of Bennett et al and mine as both being entanglements of formation. However, I make VERY clear in the paper that I am calculating squashed entanglements.

The computer that I was using circa 2003 crashed and I didn’t backup the emails. However, anybody interested in the truth can check the following facts:

(a)

THE CHRISTANDL/WINTER PAPER IN ITS FIRST VERSION (16 Aug 2003) CITES 2 OF MY PAPERS(b) The paper

http://arxiv.org/abs/quant-ph/0304007

by Patrick Hayden, Richard Jozsa, Denes Petz, Andreas Winter

came out BEFORE the Christandl/Winter paper. The first version of quant-ph/0304007 (1 April 2003) does not mention my work, whereas its second version (Aug 22, 2003) does. Why is that? Because shortly after the first version, I emailed to ALL FOUR authors (or at least most of them, I can’t remember if I was able to find the email address of all 4, but I’m sure I succeeded in finding most of the 4 if not all of them)

In light of (a) and (b), for Winter to claim that he didn’t know about my work when he wrote his paper with Christandl is creepy.

Comment by rrtucci — October 17, 2013 @ 8:12 am

I will now address all of these points, as there is clearly still some confusion.

1) As we have said, it was not our intention to hurt your reputation. There are many similar instances like this that have occurred before. Many people defined the quantity now known as the Holevo quantity and had conjectures about it, but it was Holevo who proved that it serves as an upper bound on the accessible information. As a result, it is now the case that this quantity is known as the Holevo quantity and the bound known as the Holevo bound. The followup papers now just cite the work of Holevo since his was the most important insight here. Do you think that the authors who defined the Holevo quantity but are not getting cited now are frantically emailing every author of every followup paper and writing blog posts about including a citation to their work? In 2008, Hastings proved a counterexample to the additivity conjecture by building significantly on the work of Hayden and Winter. From your perspective, if you would be in the place of Hayden and Winter, it seems that you would view the proof of Hastings to be some trivial modification of your own ideas, when in fact the work of Hastings went significantly beyond the prior work and had to introduce a new conceptual approach. The citations now go to Hastings for developing these ideas with very few citations going to the prior work of Hayden and Winter. Do you think that Hayden and Winter are emailing all of the authors of these citing papers or are blogging about including citations? The list goes on and on… However, we have now cited you in our paper.

2) You’re still failing to recognize the subtlety and importance of the issue. To state things again, with a minimum in the definition of squashed entanglement, it’s not clear whether the resulting quantity is an entanglement measure. With an infimum in the definition, Christandl and Winter proved that it satisfies many of the properties of an entanglement measure and followup work proved that it satisfies all of the other properties (again only if an infimum is there). A minimum would require there to be a smallest element in the set, whereas an infimum is just the greatest lower bound. As I said in my blog comment, it very well could be that a minimum suffices, but this is an important open question which your papers, the Wikipedia article, your blog post, and your followup comments dismiss as irrelevant. Regarding the Shannon comment, this is an issue that Shannon would have recognized. Furthermore, I was not claiming that *I* was the one who recognized the importance of the infimum / minimum issue, but rather it is something discussed at great length in the Christandl-Winter paper. Finally, it is well known that the infimum in entanglement of formation can safely be replaced by a minimum.

3) You’re still missing the point on this one as well. Without a bound on the dimension of the extension system, will your C++ computer program ever stop running? If not, is it a useful program? This is the meaning of the point about it not being clear whether the computation of the squashed entanglement can be performed in nondeterministic polynomial time.

4) I see this now. This must have been a simple oversight with Winter in our email exchange. He was coauthoring two related papers at the time. Hayden et al. were unaware of your paper, but eventually included a citation. Christandl and Winter then included a citation to your paper. Finally, we have now included an appropriate citation to your work in our paper.

Comment by Mark M. Wilde — October 17, 2013 @ 1:13 pm

[…] Peter Woit continues the heretical work he started with his 'Not Even Wrong' book, Robert R. Tucci fiercely defends his quantum algorithm work when he feels he is not credited, Sabine Hossenfelder had to ban a highly qualified String theory […]

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