Science

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Bell tests

The loophole free Bell experiments are among the top achievements in quantum information science over the last few years. However, as with other recent experimental validations of an a well accepted theory, the results did not change our view of reality. The few skeptics remained unconvinced, while the majority received further confirmation of a theory we already accepted. It turns out that this was not the case with the first Bell tests in the 1970s and 1980s (Clauser, Aspect etc. )

Jaynes, a prominent 20th century physicist who did some important work on light matter interaction did not believe that the electromagnetic field needs to be quantized (until Clauser’s experiment) and did extensive work on explaining optical phenomena without photons. As part of our recent work on modeling a quantum optics experiment using a modified version of classical electrodynamics (and no `photons’) we had a look at Jaynes’s last review of his neo-classical theory (1973). This work was incredibly impressive and fairly successful, but it was clear (to him at least) that it could not survive a violation of Bell’s inequalities. Jaynes’s review was written at the same time as the first Bell test experiments were reported by Clauser. In a show of extraordinary scientific honesty he wrote:

If it [Clauser’s experiment] survives that scrutiny, and if the experimental result is confirmed by others, then this will surely go down as one of the most incredible intellectual achievements in the history of science, and my own work will lie in ruins.

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Three papers published

When it rains it pours. I had three papers published in the last week. One experimental paper and two papers about entanglement.

  1. Experimental violation of the Leggett–Garg inequality in a three-level system. A cool experimental project with IQC’s liquid state NMR group.    Check out the outreach article  about this experiment.
  2. Extrapolated quantum states, void states and a huge novel class of distillable entangled states. My first collaboration with Tal Mor and Michel Boyer and my first paper to appear in a bona fide CS journal (although the content is really mathematical physics). It took about 18 months to get the first referee reports.
  3. Entanglement and deterministic quantum computing with one qubit. This is a follow up to the paper above, although it appeared on arXiv  a few months earlier.
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Nonlocal Measurements

My paper Nonlocal Measurements Via Quantum Erasure has  finally been published in PRL.  There is a short news story on the work on the IQC website. I also recently wrote a related blog post on nonlocal measurements for the IQC blog.

IQC blog post: Tomaytos, Tomahtos and Non-local Measurements

 

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Nonlocal measurements via quantum erasure, A. Brodutch and E. Cohen  Phys. Rev. Lett 116 (2016)

 

 

Photons in curved space-time
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Photons in curved space-time

The IQC blog “Our quantum world” is finally open. The first blog post is about possible experiments that can detect the effect of Earth’s gravity on photons, check it out.

You can also check out my papers with Daniel Terno and other collaborators on the subject.

Polarization rotation, reference frames, and Mach’s principle

Photon polarization and geometric phase in general relativity

Post-Newtonian gravitational effects in optical interferometry

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Writing a PRL comment.

Getting a comment published  in PRL is far from trivial. I recently succeeded in publishing my Comment on: How the result of a single coin toss can turn out to be 100 heads.  Despite the fact that I pointed out a major  error in a published paper, the road to publication was long and difficult.  The odds were against me (5 other comments on the same paper were rejected despite being correct) and I had to fight the authors of the original paper on top of a biased editor and a referee.   I hope this post will help anyone  thinking about writing a comment (or a reply to a comment).  This was my second attempt at a PRL comment, the first one did not get published as a comment but eventually became a very well received paper.

I attempted to be as general as possible and minimize the specific technical details of  my comment. For anyone interested in the content, the arXiv version is slightly more complete.  It contains a one paragraph response to the published reply. This short response is a very good summary of the comment.

Publishing a comment in PRL

1. A PRL with errors

So you think PRL XXX has mistakes and makes false claims, and you think you should let the world know. What better way than submitting a comment in PRL?  Well… You’re in for a treat.

Generally PRL will only publish a comment if it identifies a central error. This has  following implications: If the paper in question is completely meaningless it cannot contain an error and is therefore comment-proof. If the discussion of the results is speculative to the point where it is not supported by the results of the paper, it is also safe, unless you can convince the editor that the discussion is a central point. etc..

Example 1: The paper I commented on made absurd claims such as:

Our results provide evidence that weak values are not inherently quantum but rather a purely statistical feature of pre- and postselection with disturbance

such claims, although unjustified, are unfortunately safe from comments since it is almost impossible to demonstrate they are the central point of the paper.

My guess is that the majority of the five or six comments submitted on this specific paper were rejected for this reason. Each comment (e.g 1,2,3,4) showed that central features of weak measurements were missing in the supposed `classical analogue’. The relation to weak values is so weak that all subsequent conclusions about the nature of weak values are speculative at best.  But wild speculation is not a central mistake and the claim is safe from criticism in PRL.

Technical note: I commented on a paper that supposedly provided a classical analogue for anomalous weak values. The central result of the paper was a measurement scheme that provides strange results which they claimed are classical weak values. Most of the other comments showed that the scheme is not a weak measurement in one way or another. My comment was different in that I simply showed that they are using a nonsensical method to calculate the result of the measurement.

2. You will probably end up fighting with both the referee and authors of the original paper

Before submitting your comment, you may want to contact the authors of the original paper to see their reaction. I guess that in some cases scientists will put science ahead of their ego, but in many (most?) cases they will not. The result is that they will try to fight the comment. You should be aware of this.

The editor also has an ego. He accepted the paper and he does not like to admit he accepted a paper with a major mistake (remember PRL only accepts comments that point out central errors).

After you submit the comment, the editor will usually send it directly to the original authors (the other option is a quick reject). They will then write a report claiming that your comment is not worth publishing.

Here you are at a disadvantage. The editor will probably side with the authors. The likely outcome is a reject or (as in my case) a “we cannot accept” unless you make a good rebuttal.

Example 2: A few years ago we tried to write a comment on a paper titled “Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps“. We provided a counterexample to the statement in the title. The main objections of the authors were that we were working under different assumptions. WTF? There were no explicit assumptions in the paper (or in the preceding literature) that contradicted our counterexample, moreover they never event attempted to point out what the different assumptions were. Nevertheless the editor agreed with the authors. The counterexample never made it as a comment (despite going through phase 3-4 below), but did eventually turn into a very nice paper.

3. The rebuttal

If things went well, this is the point where the editor asks for a rebuttal of the claims in the informal reply. Now, here is the most important piece of advice. Do not make any changes to your comment at this stage! Just as the authors try to show that your comment is a piece of junk, you should at this point show that their reply is a joke. Remember, the authors are not your friends, they are not trying to improve your comment, they want it out of their way.

So you need to plan ahead. When submitting the comment you must anticipate all possible replies by the authors. If your argument is correct, and furthermore if you hit a mistake that may be considered critical, the rebuttal should not be a major task. This is what I learned from my previous experience and it paid off.

One issue that appeared in all author responses (to this comment and the previous one) was misdirection. On top of the attempt to show that the claims are not a central issue, the authors try to misdirect the editor/referee and move the argument in a different direction.  The best advice is to try and ignore those issues that are tangential to your central claim.

Example 3:  In both the informal and published reply, the authors claimed that there are other papers with classical analogues of weak measurements. The issue has little to do with my comment. My comment was: There is a mathematical error in this paper. I don’t really care if some other guys have similar results. I never responded to that criticism.

4. If you were successful with your rebuttal, your paper will be sent to a referee

The referee will give you comments on your manuscript. Treat them like any other referee reports. In my case they made very good points and asked for clarifications and changes before making a decision. I made the changes and the paper is much much better as a result.

It is perhaps important to remember that the referee will get some of the editor’s bias, in-fact in my previous comment we got the following negative report “I agree with the editor”.

5. Back to the authors

And again they get to reply, and again they can make it as long as they want.

I was reasonably lucky at this stage because the authors are not experts in the field and it was very easy to point out mistakes in their reply. As before, I did not make any changes based on the author’s reply, and only responded to real criticism.

The paper went back to the referee and he made some suggestions on possible changes but otherwise recommended publication.

6. The reply

At this point the authors had to give their one page reply. This reply did not go to referees. It was sent to me, but the editor explained that it will be published regardless of what I say. My only reply was to point out two technical errors. The authors quoted some results that do not exist and are plain wrong (in fact they base their argument on an inequality where the units don’t match).  The editor was nice enough to let me add a (very brief) note to the comment pointing out these errors. He was also nice to the original paper’s authors and allowed them to make the same type of change (but nothing else), i.e add a note at the end of their paper. Their note contained another mistake (actually the same mistake again) and subsequently they now have a reply with three major technical errors.

This is a lesson for anyone writing a reply. It might not be refereed so make fucking sure it is all correct. One way to get some feedback is to use similar arguments to the ones used to fight the comment. If you make up new things at the last moment you are risking it.

Since there was no option to react to their reply, I added a short response on the arXiv version. Actually this short response is better than my comment and it is a shame it would not get published, but such is life.

7. Have fun

If like me, you like a good argument, a comment is an extreme challenge with a referee to help decide the winner. At the end of the day (actually months) the back and forth can be enjoyable. On top having to make concise and precise arguments I  had to read the literature presented in the counter-arguments, this forced me to read some  nice papers that I had been putting off for a while, or missed.  Moreover, each time  it was great to learn how well I anticipated the  attempts at refuting my comment (I did not anticipate the  mathematical mistakes that appeared in  the published reply).

 

8. Conclusion

Writing a comment can be a very rewarding experience, especially if it gets published. On the other hand, comments are a lot more work than you would expect. The process is ugly and biased against the person making a comment. As a rule, PRL editor try to fight off comments and make to road to publication tough. The upside is that getting it published is extremely gratifying.

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Discord and completely positive maps

After over two years of work  we finally published our results showing that the connection between discord and complete positivity is quite weak, and probably has no operational significance. But let me start at the beginning:

In the beginning… and then there was a big discussion/argument about possible maps describing the evolution of a quantum system interacting with the environment. In the case where they are initially correlated this discussion is still not settled. In 2007 came a paper by Cesar Rodriguez-Rosario Kavan Modi, Aik-meng Kuah, Anil Shaji and ECG Sudarshan titled “Completely positive maps and classical correlations“, I call it Cesar and Kavan’s paper. They examined a situation where some initial family of system-environement, $$mathcal{SE}$$ states is classically correlated (has zero discord). It turns out that such a family of states is in the consistency domain of  a completely positive assignment map. In slightly less technical language: given a family of classically correlated $$mathcal{SE}$$ states it is possible to describe the evolution of the system using a completely positive map. Without going into details this comes with some caveats. Cesar, Kavan and Alán Aspuru-Guzik explained these caveats in another paper.

About a year after Cesar and Kavan’s paper Alireza Shabani and Daniel Lidar published a paper titled “Vanishing Quantum Discord is Necessary and Sufficient for Completely Positive Maps” This result was published in PRL, I will call it the SL paper. It made a lot of waves and has since been cited around 150 times. Unfortunately no one really understands it. I don’t know who should be blamed here, the authors for writing an unreadable paper (I assume they can read it), the editor for accepting an unreadable paper, or the referees who thought the paper was readable. But as it stands this paper was accepted, and since it was published in a prestigious journal and has such a bombastic title, people love to cite it. Especially to justify their research on discord. I guess I could start a rant but it’s nothing new so let us return to the story.

In September 2010 I had the extreme pleasure of attending the “Quantum Coherenece and Decoherence” workshop in Benasque where I met Cesar and Animesh Datta. After a short conversation about discord and interesting results in the field we discovered that although we have all cited SL we don’t know what they actually claim. We all assumed it was the “necessary” part of Cesar and Kavan’s “sufficient” result for completely positive maps but none of us could really explain the bottom line. After spending a few days in trying to understand the paper together we finally gave up, and instead came up with a counterexample. That is, we found a family of discordant states which is consistent with a completely positive assignment map.

A few weeks later I met Kavan in Singapore and we discussed this result further…

[missing reel]

.. and finally  Ángel Rivas joined our jolly group. The work was very slow, mostly due to us being on 4 different continents. By the time time I was at IQC we had a draft. When Kavan came to visit we finalized the paper.

The final version is much more then a comment on SL’s result. We showed that the problem of finding the map that correctly describes the evolution is a matter of how the problem is stated. More to the point, we showed that in at least thee sensible frameworks for approaching this problem there is at best a one way connection between positivity of the map and discord. Presumably there might be a framework where zero discord is both necressary and sufficient for completely positive maps. Unfortunately we were unable to identify this framework.

 

Vanishing quantum discord is not necessary for completely-positive maps
Aharon Brodutch, Animesh Datta, Kavan Modi, Ángel Rivas, César A. Rodríguez-Rosario arXiv:1212.4387, Phys. Rev. A 87, 042301

 

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Quantum discord

After a long an eventful month that included a visit by Kavan Modi to IQC and my visit to Israel (I’m posting from Israel), it’s time I got back to writing something. This time I’ll say something about my work for the past four years (as promised). One of the main subjects of my research is quantum correlations, and their role in defining the difference between quantum and classical (not quantum) systems.
Imagine a piece of information shared between two people Alice and Bob. Now think of a way to quantify the correlations between them. One way to quantify correlations is to ask what can Alice know about Bob’s part of the information by looking at her own part.
For example lets say Alice and Bob are each given a queen from a chess board. Alice then looks at her queen and sees it is white. She now knows Bob’s queen must be black. Alice and Bob are strongly correlated, since Alice always knows Bob’s piece by looking at her own.
For the second example Alice and Bob are each given a queen, but this time from a Deck of cards. If Alice sees a red queen she can say that it is more likely that Bob has a black queen, but she has no certainty. Correlations are lower in this case then in the chess example.
There is another way to account for correlations. We can ask about difference between the information in Alice and Bob’s hands individually and the information in their hands together. In the chess example Alice and Bob can each get one of two types of queens: black or white Together they also have two options Black White or White Black.
It turns out that both options for quantifying correlations are the same. To see this in the example we need to quantify the information in bits. Since Bob has two options in his hand “black queen” or “white queen” he has one bit of information. The amount of information Alice can discover about Bob is precisely this one bit. So they have one bit of correlations. Alternatively we can say that Alice has one bit of information: “black queen” or “white queen”; Bob has one bit of information: “black queen” or “white queen” and together they also have one bit “black white” or “white black”. The difference (1+1)-1 is again 1 bit so there is one bit of correlations.
Since i’m avoiding maths you will have to take my word that both methods give the same result in all cases… in the classical world. In the quantum world things are a bit different.
There are two essential (and related) aspects of quantum theory that make these two ideas about how to to quantify correlations give different results. 1) Measurements affect the system. If Alice wants to know the color of her queen, she needs to make a measurement, this measurement can change the state of the system; and 2) Quantum systems can be correlated in a much stronger way then classical systems, a phenomenon known as entanglement.
Before discussing the first aspect in detail, I will say a bit about entanglement. Entanglement was a term coined by Schrodinger in his famous “cat” paper, this paper was inspired by the earlier “paradox” of Einstein Podolski and Rosen (EPR). They showed that quantum mechanics predicts a situation where a system shared by two parties is in a well defined state although locally it is not defined. A system is in a well defined state if making a measurement on this system will give some result with certainty. So if I give Alice and Bob an entangled system I can predict the result of a measurement made on the whole system, but I cannot predict the result of a measurement made by Alice and Bob separately.
Entanglement is the most remarkable prediction of quantum mechanics, and in one way of another it is the driving force behind most of the really cool quantum phenomena. From quantum computers to Schrodinger’s cat. Nevertheless entanglement does not account for all the non-classical features of the theory. At least not directly. When discussing correlations, measurements and their effects on the system play a crucial role in describing non-classicality. To explain quantum measurements we can imagine a quantum system as an arrow pointing to some direction, X, in the simplest case we can think of this problem in two dimensions.
A quantum measurement is a question regarding the direction of the arrow. Is the arrow pointing in direction A? This has one of two results either yes or no. The probability is given by the angle between the “actual” direction and the direction in question. The effect of the measurement is that the arrow will now point in the same direction as the result. If the answer is yes it will point in direction A if the answer is no, it will point in the opposite direction.

 

A quantum measurement will "collapse" the state X into A or Not A.

A quantum measurement will “collapse” the state X into A or Not A.

Ok so what does this have to do with correlations? Well lets go back to the two definitions for correlations. The first was “What information can Alice find about Bob by looking at her own system”. In the quantum case this is no a clear question, we need to also say what measurement Alice is making. Different measurements will reveal different information about Bob. The second definition for correlations is what is the difference between the information in Alice’s hands plus the information in Bob’s hands and the information in their joint system” This is not directly related to measurement, so clearly it is not the same as the first definition. The difference between these definitions in the quantum case is the quantum discord. It is a measure of the “quantumness” of correlations.
As it turns out discord can be found in many interesting quantum systems and paradigms, but it is not yet clear what this means…

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I’m an expert

Two expected, but long awaited events happened on my birthday. One: I found out that my Phd was approved, so no more bureaucratic shit regarding that. Two: The review paper on discord and similar quantities was finally published. This sums up about one and a half years’ work spent on reading, writing and rewriting this review with my collaborators.  Two versions have been posted on  arXiv  since the end of last year. The latest one, posted in August, is pretty much the published version.

I will soon post something longer about discord and non-classical correlations, for now it is enough to say that quantum theory allows more general correlations then a classical theory.  Entanglement is the best example of these types of correlations, but as it turns out there are unentangled systems with non-classical correlations. Quantum discord captures entanglement and more (but not everything).

Since the beginning of the century (i.e 12 years ago) people started studying these kinds of correlations “beyond” entanglement in various forms and physical scenarios. The area exploded about 5 years ago and discord became a “hot” topic. The review includes almost all the work done on the subject until the end of 2011. discord was studied in so many different scenarios like quantum information, thermodynamics, many body systems, relativistic quantum information and others which made work on this review so much fun, on the one hand, but a lot of work on the other.