## Uncertainty relations for angular momentum

September 29, 2015

I’m excited to share with you today a video

by Lars Dammeier, Rene Schwonnek, and Reinhard F. Werner of the Quantum Information Group Hannover, This video is intended as a video abstract for their recent paper of the same name which you can find at New J. Phys. 17 (2015) 093046 (http://dx.doi.org/10.1088/1367-2630/1…, and http://arxiv.org/abs/1505.00049). I had the great pleasure of helping in the production of the video (in this case I took care of the filming and post-production).

This video was directly inspired by the fabulous minutephysics https://www.youtube.com/user/minuteph…
and Vsauce

If you like this kind of thing and want to see more then please do hit the like button to let us know or, better yet, subscribe.

## Entropic bounds on the quantum marginal problem

September 22, 2015

### Do you want an easy simple way to bring your work to a wider audience?

Yes, yes, and yes!

I am always on the lookout for cheap, easy, and painless ways to avoid hard work. Thus it was that I had the idea of making videos explanations of old unpublished results: I figured that since it is really easy to explain something on a board, it must follow that with a cheap video camera and a spare 20 minutes it must be easy to make videos.

Well, ok, it turns out that it isn’t so simple because it is actually rather hard work to make a not-complete-piece-of-crap video.

Today I’d like to announce a youtube video experiment aimed at finding a good way to communicate unpublished results that are still interesting. The purpose of this video is to explain the basic idea behind a paper I wrote in 2008 that I feel, sadly, will never be published (due in part to unbelievably hostile referee reports and a subsequent lack of motivation on my part). The paper in question contains a simple bound on the number of independent solutions to the quantum marginal problem, which is of central importance in quantum information theory.

If you are interested in learning more about the quantum marginal problem I can happily recommend checking out this talk and this blog post. Also take a look at this thesis and overview, the gaussian version, a powerful solution, and an intuitive solution of the simple subcase. Also check out this cool application. There have been some further progress on using entropic bounds in this recent paper.

Sadly the video production equipment I had on hand simply wasn’t as good as it should be: I’ve now learnt the hard way that one should invest in a good microphone and a camera that isn’t 8 years old… (Probably a smartphone would’ve done a better job…) I’ve since corrected this and in my next videos I hope to improve the sound and picture quality to at least an acceptable level…

Please like the video if it is something you want to see more of, dislike it if you think it was terrible, and please do subscribe if you want to see more!

## Presentations are more important than papers: my first youtube video

July 27, 2015

During the past 5 years or so I have come to believe that presentations are actually more important than scientific papers. As a consequence, I have recently spent quite a lot of energy learning how to give better presentations. This is a truly fascinating and rewarding topic. While I find it is difficult, if not downright impossible, to master good public speaking, I’ve very much enjoyed trying to improve how I give my presentations.

Today I’d like to annouce the appearance of my first youtube video:

This is a recording of a talk I recently gave to graduate students here in Hannover. The objective of the talk was to share and channel advice I’ve received in the past years on how to give a good presentation. While I don’t claim to be especially good at giving good talks myself (the excruciating experience of watching myself on video for essentially the first time only serves to underline this!) I have learnt a great deal from other excellent speakers, and I hope that I can at least share a couple of the tips and tricks I’ve learnt.

Depending on the reception to this video it might signal a change in the way I will go about communicating our research. I’ve recently noticed that I am spending an increasing amount of time watching videos of talks at conferences, video tutorials, and miscellaneous other videos (cat videos, unboxings, etc. :) ). It truly is a supremely powerful medium of communication, combining both visual and auditory modes of delivery, and, given that you can pause and skip, I have found it to often be superior to attending talks.

I am still passionate about open science, and open notebook science, and I am always contemplating better and more efficient ways to implement at least some core principles of openness. This is why this blog and my twitter account have become so neglected as of late: I’ve just found that github provides an amazingly useful, superior, and simple tool to achieve this. If you want to know what I’m doing on any given day then you can check out my activity there. (Basically all of my notes are now stored openly there.)

However, github is not the right tool for communicating and sharing ideas. Here I think video is superior, and youtube a natural platform. We’ll see.

I do hope you enjoy watching my video; any comments, suggestions, and criticisms are (actually) welcome!

## Ideas

November 22, 2014

I’ve recently been pondering this picture

(Yes, I used comic sans. For a reason.)

## The best advice I ever got

May 27, 2014

“It’s better to pursue one bad idea to its logical conclusion than it is to start and not finish ten good ones,” Michael said.

I was sitting in Michael Nielsen’s office at The University of Queensland: it was early 2002 — a steamy Brisbane summer afternoon — and the air conditioner struggled to cool the room. I had just finished with a long despairing complaint about the disappointing lack of progress I’d been making on my PhD when he issued me with his advice. (I was beginning the third and final year of my PhD.)

I’d had an interesting ride so far: I began my PhD in the year 2000 in applied mathematics studying free-surface problems in fluid mechanics. Fluid dynamics is a challenging and mature research area and requires a lot of effort to get up to speed. Unfortunately, I am very lazy and it had taken me a very long time. Also, I quickly found out that I just wasn’t that interested in the motion of fluids (although, one of the papers I’m proudest of emerged from this period). I quickly became unmotivated and I had begun to distract myself by reading quantum field theory textbooks to procrastinate instead of finding that sneaky bug in my code…

Then everything changed. I think it was in late 2001 when Michael arrived at UQ and gave a series of talks on quantum computers. I was hooked and I immediately dropped everything and started working with Michael “in my free time” on quantum entanglement and condensed matter systems.

I once heard a definition of a golden age in science as a period when mediocre scientists could make great contributions. (I forget when and where I heard this and a cursory google search didn’t turn up anything.) The early 2000s were definitely a golden age for quantum information theory and I had the greatest luck to work with one of its architects. In practically no time whatsoever (in comparison with applied mathematics) we’d written a couple of papers on entanglement in quantum phase transitions.

It had been just so effortless. Now I’d finally found a research field that appealed to me: with an absolute minimum of effort one could write a paper that’d be read by more than two people. Wow! (Alas, this is no longer true…)

All this went to my head. I figured that if one could just stick two buzzwords together (entanglement and quantum phase transitions) and get a paper then why not do it again? I was skimming through texts on partial differential equations, algebraic topology, and stochastic calculus and seeing connections EVERYWHERE! I was discovering “deep” connections between entanglement and homotopy theory before breathlessly diving into an idea for a quantum algorithm to solve PDEs. I would spiral into hypnotic trances, staring distractedly into space while one amazing idea after the other flowed through mind. (This is the closest I ever got to the flow state so beloved of hackers.)

But at the same time frustration, edged with desperation, was growing. I was having all these amazing ideas but, somehow, when I started writing one of them down it started to seem just sooooo boring and I promptly had a better one. My hard drive filled with unfinished papers. I had less than a year until my money was gone and no new papers!

I was lost in the dark playground:

I then went to Michael and told him of my frustration. And it was this complaint that had prompted him to give me his advice. All at once, it was clear to me what I’d been doing wrong. So I threw my energies into a problem Micheal suggested might be interesting: proving the general Coffman-Kundu-Wootters inequality. This was a hugely satisfying time; although I didn’t end up proving the inequality during my PhD I managed to, mostly by myself, work out a generalisation of a formula for a mixed-state entanglement measure that I was convinced would be essential for a proof (this sort of thing was a big deal in those days, I guess not anymore). Every day I was tempted by new and more interesting ideas, but I now knew them for the temptation of procrastination that they were.

Michael’s advice has stuck with me ever since and has become one of my most cherished principles. These days I’m often heard giving the same advice to people suffering from the same temptation of the “better idea”.

Now “focus on one idea” is all very well, but which idea should you focus on? (You will have no doubt noticed that I was rather lucky Michael had the perspective to suggest what was actually a rather good one.) What do we do if we have lots and lots of good ideas, each one of them clamoring for attention? How do we break the symmetry? How can we best choose just one or two ideas to focus on? How should you split your most precious resource, your time, while balancing the riskiness of an idea against its potential return?

Ultimately I do not have an answer, but I do have a decision tool that can help you to make your mind up. The idea is to regard research ideas as investments, i.e. assets, and to evaluate their potential return and their risk. In this language we have reduced the problem to that of investing some capital, your time, amongst several assets. This is an old problem in portfolio management and there is a very nice tool to help you work out the best strategy: the risk-return plane. The idea is pretty simple. In the case of portfolio management you have some capital you want to split amongst a portfolio of assets which are characterised by two numbers, their average return and their risk, i.e., the standard deviation of their return. Take a two-dimensional plane and label the x-axis with the word “risk” and the y-axis with the word “return”. Each asset is plotted as a point on the risk-return plane:

Now something should be obvious: you should never invest in an asset with the same return but higher risk, nor should you ever invest in an asset with the same risk but lower return. This picks out a thin set of assets living on the “boundary” of (basically the convex hull of) all the assets, called the efficient frontier. You should only ever invest in assets on the efficient frontier.

For a joke I once suggested using the risk-return plane to work out what research idea you should work on. However, it quickly became apparent that some people found it a useful tool. Here’s one way to do things: first write down all your research ideas. Then, after some honest reflection on what you think the most likely outcome of a successful result from the project would be, associate a “return” to each idea. (Just ask yourself: if everything worked out how happy would you be? How much would the completed idea contribute to science? Insert your own metric here.) The way I did this was, somewhat flippantly, to label each idea with a journal that I thought would accept the idea. Thus I created a list:

1. Journal of publish anything
2. Physical Review
3. New Journal of Physics
4. Physical Review Letters
5. Science, Nature, Annals of Mathematics, etc.

It is totally silly but it has just sort of stuck since then. Next, you have to assess the risk of each project. I think a reasonable way to do this is to quantify each research idea according to what you think is required to solve it, e.g., according to

1. Trivial calculation
2. Longer calculation
3. Some missing steps
4. Needs a new technique
5. I don’t know anything of what’s required

For an example let’s just take a look at my top twelve research ideas for the last year:

1. Chern-Weil theory applied to classification of quantum phases via quasi-adiabatic continuation.
2. Reaction kinetics for ultracold chemistry.
3. Continuous limits for quantum lattice systems.
4. Tensor networks for lattice gauge theory.
5. The scattering problem for local excitations in lattice systems.
6. Prove the quantum PCP conjecture.
7. Improve the gap for adiabatic quantum computation.
8. K-theory for the MREGS problem.
9. Classify topological order in higher dimensions.
10. A compact formula for the distillable entanglement of two qubits.
11. Calculate the entanglement of the 2-rotor rotor model.
12. Prove the quantum version of the KKL inequality.

Here’s my risk-return plane:

Looking at the results it quickly became apparent that I shouldn’t really invest my energy in a formula for the 2-qubit distillable entanglement (shame! I would be interested in solving that one, but I just can’t see how it would be useful to anyone, including to myself!!!) Also, I should steer clear of the quantum KKL inequality, the quantum PCP conjecture, and K-theory for MREGS.

Note that all of this is completely and utterly subjective! You might well argue that a proof of the quantum PCP conjecture would be a tremendously impactful result on par with the quantisation of quantum gravity. But my purely subjective assessment at the time was that it would not be of the same level of impact (for me) as, say, classifying topological order in all dimensions.

Thus, out of the top 12 ideas floating around my head only 5 remained. This is still way too many! To winnow down the list it is helpful to use an investment strategy employed in portfolio management which is, roughly speaking, to invest a more of your capital in less risky assets than riskier assets (i.e., don’t put all your eggs in one risky basket!!!!) Thus I dropped the riskiest idea and I also dropped the most trivial one as not really giving much personal reward. I was left with three ideas. This was just about enough for me, and I spent most of my available energies on those.

I find it helpful to keep this risk return plane around and to periodically update it as I get more information, or when I get new ideas. Looking at it today I figure I’ll move the adiabatic gap, Chern-Weil theory, and the scattering problem ideas up a bit. Maybe I’ll work on them soon…

## An introduction to the continuous limit construction I

May 19, 2014

In this post I’d like to begin to explore what is meant by the continuum limit of a quantum lattice system. This post is meant to serve as the first in a series of intuitive overviews of the ideas involved in the open science project “continuous-limits-of-quantum-lattice-systems” hosted on github.

The continuous limit is a power tool in the condensed-matter theorist’s toolkit: by identifying the appropriate effective field theory modelling the low-energy large-scale physics of a complex quantum system one can bring the fully developed apparatus of (perturbative) field theory and the renormalisation group to bear on a problem, often delivering results unavailable via any other means.

Now I’m pretty sure I’m not alone in feeling confused by much of the available physical literature on this topic. Over the past decade I’ve tried to understand the process whereby a field theory is produced to describe a given quantum lattice system. However, up until recently, this has always seemed like a kind of mysterious black magic to me. I know it has to do with symmetries etc. etc.. But this didn’t really help me! I had so many questions. E.g., how exactly does the state of the effective field theory relate to that of the original lattice system? And, for that matter, how do you know what quantities are “fieldlike” and which don’t admit a field-theoretic representation? That is, what has most puzzled me is the quantitative side of things: ideally what I would like is some kind of map which associates, one to one, lattice quantities with field quantities in an operationally transparent way.

Thus I was very excited when I discovered that there is indeed such a map and, further, is naturally associated with the quantum de Finetti theorem. Here I’d like to explain the idea behind this construction using the quantum information theoretic language of exchangeable states.

## Dreams: they do not work for me!

May 7, 2014

There are several stories of great discoveries been made in dreams (see this wonderful wikipedia list for some famous ones).

Unfortunately I have never had the good luck to have a dream which gave me a creative insight to solve a problem. That isn’t to say that I don’t dream about my research. Last night, for instance, I dreamt of classifying two-dimensional quantum phases using a quantum generalisation of the j-invariant and some other invariant which I, in my dream, for some reason wrote as $|C|$. When I woke up I quickly checked whether any sense could be made of this. As usual, far as I could see, it is total nonsense. Sigh.

I’ve also been rather envious of those who seem to be able to exploit unconscious cognition. When I was doing my PhD, I was mightily impressed by Michael Nielsen who would sometimes pause in the middle of a conversation and exclaim “I now know how to solve problem x!”. I mean, how cool is that!? Alas, it never worked for me. Oh, I do get “aha” moments rather often, but the result is usually complete junk…

I only get results after hard slog. I have to make lots and lots and lots of mistakes and only then, slowly and gradually, the result emerges, reluctantly and complaining all the while, in its final form.

I can’t remember ever really experiencing a dream or an “aha” moment that turned out to be really correct.