Research lines that lead nowhere (I): Quantum Discord

Hi rats,

These days I’ve been searching in the garbage bin (i.e., arxiv) for a nice topic to chew. I didn’t have to dig deep. A preliminary search shows that only this year there have been uploaded 129 articles on quantum discord, and the number is growing as I write this post. This puts discord into the category of pandemic. The stakes are high: if we don’t act soon, quantum discord could destroy thousands of promising scientific careers, and possibly even cause the end of civilization!

But let’s go by parts.

The quantum discord of a bipartite state was first defined by Ollivier and Zurek as the difference between its original quantum mutual information and the same quantity after we perform a rank-1 projective measurement on one part. 

Now, what does that mean? Probably, nothing. But lack of motivation has never prevented investigation at international scale. And so we ended up with one more research topic that clearly goes nowhere, in the line of entanglement sudden death, NMR quantum computing and quantum game theory (ah! You don’t remember quantum game theory? Then suffer!!).

The first victims of the epidemic were the hundreds of PhD students who were forced to calculate quantum discord in the weirdest physical scenarios: ground states of inexistent spin chains, non-inertial frames, cavity QED, nuclear spins… This extraordinary proliferation of unnecessary calculations may remind some of the negativity fever we experienced in QI just seven years ago. There, the goal was to compute the negativity of every bipartite two-level system in the Universe, and their proponents nearly succeeded at this task.

[A reflexion: if you are not sure about the meaning of a quantity, is it worth calculating it?]

Nevertheless, there is a big difference between entanglement and quantum discord.

An experimental demonstration of entanglement can be quite challenging, both for the experimentalist and the theorist. Experimentally, you need a degree of control of your physical system in order to prepare the state and perform the appropriate tomographic measurements. Theoretically, you have to prove that a particular density matrix (or a family of density matrices with certain features) is out of the set of separable states, whose approximate characterization is a strongly NP-hard problem.

In contrast, as shown by Ferraro et al., the set of states with zero quantum discord has zero measure. This is very convenient from an experimental point of view, because it makes quantum tomography obsolete: any experimentalist that prepares a bipartite quantum system can immediately claim that it has non-zero quantum discord on the grounds that he was able to produce it!!

Now, you may think that the 2009 article by Ferraro et al. put a stop to discord research. That was actually the original intention of the authors (I happen to know them). However, rather than killing the bacteria, the vaccine made them stronger. Check for yourselves! The number of yearly papers on the subject has doubled since 2009. More interestingly, Ferraro et al.’s paper has now 195 citations, all from articles on quantum discord.

How can that be? I recently witnessed a talk about discord where this paper was cited. Naturally, I was curious about why someone would like to mention a paper that discredits all his research. This is the explanation I got:

“Ferraro et al.’s result shows us that discord is everywhere. Consequently, discord is at the heart of every quantum communication protocol”.

Now THAT is an argument! Let me rephrase it in a more casual way:

“Dude!! This is amazing!! There is discord between your mouth and my penis!!!”.

Unfortunately, the fact that everything has discord erases the meaning of the quality “non-zero discord”. Imagine a world where everybody is blonde. Would the word “blonde” have a meaning? Wouldn’t it be like “wireless”?

A world where everybody were blond could be very spooky.

One of the latest mutations of The Plague has the form of papers “proving” that certain separable states with non-zero discord constitute a resource in bipartite communication protocols. The truth is: that can only be true in very artificial scenarios. First, if your figure of merit depends linearly on the initial state, or is just convex, any result you may achieve with a separable state (with zero or non-zero discord) can be equalled or improved with a pure product state (of zero discord). Second, even if your figure of merit is not convex, any communication protocol with steps 1, 2, …, n that requires a separable state rho with non-zero discord at step 1 can be implemented too if, at the beginning of the protocol, both parties share a correlated classical state (of zero discord) and use the classical correlations of their zero-discord state to prepare rho locally before proceeding to step 1.

Rats, I don’t know what to do. Men greater than this rodent have tried to stop this madness, but have failed miserably. Were they too subtle in expressing their dislike for discord? Shall we throw our excrements at the speaker’s face next time we attend a talk on the topic in order to make our point clear? I can’t say that I approve this. But, should you do it, send me the video.

Ok, I’m tired. These are the take-home messages:

1) Kids: say "no" to quantum discord! It's just not worth it!

2) Discord Stus of the world: if my arguments haven't convinced you to stop spreading your disease, then at least stop calling it "quantum correlations". The term "quantum correlations" has been disputed for many years by the entanglement and nonlocality communities. The last thing we need is a new third party messing things even more.

Yours truly,

Schroedinger’s rat

It looks like a duck, swims like a duck, and quacks like a duck. But it is actually a piece of shit.

Hi rats,

I was pondering what could the first entry of this blog be, when I bumped into this Wikipedia entry on quantum nonlocality. I immediately felt the urge of discussing a paper which caused a big fuss in the Quantum Information community two years ago. I’m referring to “The Uncertainty Principle Determines the Nonlocality of Quantum Mechanics”, by Jonathan Oppenheim and Stephanie Wehner.

The paper consists in a series of lame statements, embarrassingly obvious for anybody with an interest in quantum nonlocality. However, against all oddS, the artiCle got printEd iN CErtain high impact factor journal that I will not disclose here.

Then the horror began: the authors were invited to talk about their results in several conferences in Foundations of Physics and Quantum Information (it was a featured talk at a past edition of QIP!). They were interviewed in various popular science magazines, where well established researchers praised the originality of their ideas. They were cited in respectable works in nonlocality (the paper currently has more than 38 citations, including one of mine!!! [Ah, co-authors…!]). On top of this, I suspect that they have recently been invited to write a chapter about the paper in a certain forthcoming book on Foundations of Physics…

Am I making a fuss? Could I be exaggerating? Let’s have a look at the contents of the paper.

The article deals with the otherwise interesting topic of computing the maximum quantum violation of a bipartite Bell inequality (i.e., its Tsirelson’s bound). The main idea of the paper is that, once we determine the optimal measurements of one of the parties, say, Bob, we can upper bound the maximal violation by means of what the authors call fine-grained uncertainty relations (and I and others in my small, minor community call operator norms).

And operator norms is the closest you will get to Heisenberg’s uncertainty relation in this article. Contrary to what the abstract suggests, trying to bound Bell functionals via Heisenberg-type uncertainty relations ΔAΔB≥|tr(σ[A,B])|/2 is not a very promising enterprise, because, in finite dimensions, this expression becomes trivial after eliminating the dependence on the state σ of the system (indeed, take σ to be the maximally mixed state and you will get the revealing result ΔAΔB≥0). Now, I don’t believe that the authors can derive Tsirelson’s bound from the physical principle that the product of two non-negative numbers is non-negative (if such is the case, I will eat my paper on macroscopic locality). Hence they have to resort to measurement inequalities that the bulk of the Physics community wouldn’t recognize as uncertainty relations.

Besides, and coming back to the beginning, I find problematic to determine a priori which measurements are optimal on Bob’s side for an arbitrary Bell functional. Isn’t that the main difficulty of calculating Tsirelson bounds in the first place? It seems to me that this is a paper about steering rather than nonlocality, because the knowledge of Bob’s measurement settings is taking for granted through the whole article.

But wait, there’s more. The authors go on to claim that in XOR games the bound derived through the fine-grained uncertainty relations is always tight. That is, if we knew a priori Bob's optimal measurements, we could calculate Tsirelson bounds for a family of nonlocal games for which we already know how to compute the maximal violation efficiently.

I haven’t read the Supplemental Material, but my guess is, the proof goes like this: as shown by Tsirelson, in XOR games, the optimal measurements in Bob’s side {Y_j} are of the form \sum_i c_i \sigma_i, where the {\sigma _i}s constitute a Clifford algebra and the optimal state is the maximally entangled state in whatever dimensions. Any linear combination of {Y_j}s is thus of the form \sum_i v_i \sigma_i. All Alice has to do is steer Bob’s states to positive and negative eigenvectors of the last expression in order to maximize the corresponding uncertainty relation. This she can achieve by performing a measurement proportional to \sum_i v_i \sigma_i on her side. QED.

It took me 10-11 seconds to come up with the previous argument. No wonder I sometimes have the impression that I’m wasting my time! Apparently, I could be getting six high impact publications per minute!!

Finally, the authors state the main conclusion of the article: any theory that allows Alice and Bob to violate a Bell inequality more than permitted by the fine-grained uncertainty relations requires measurements that do not respect the fine-grained uncertainty relations.

In other words: if it is raining, then it is not not raining.

Well, there you are. I have summarized the main result (and proofs) of the paper in a few paragraphs. I thus hope to have convinced you that this is NOT a deep paper. It isn’t original, either: I doubt that the “groundbreaking ideas” contained in this article (e.g., using operator norms to bound Bell violations) can genuinely surprise anyone who has thought about quantum Bell inequalities for three minutes.

Now, I do not blame the authors for submitting their article to XXXXXXX rather than the paper bin -they saw an opportunity and took it, who wouldn’t?-. I do not blame the editor who accepted the paper -the abstract contains the word “spooky”!-, or the referee who reviewed it -well, that one I blame a bit.

But I do blame the Quantum Information community. How come that this paper was accepted at QIP? Doesn’t this conference have something like referees? Didn’t those so-called “referees” read the paper? And what about all the other conferences? Is Foundation of Physics a real science, when their members cannot distinguish solid material from smoke? Most importantly: how could the audience of these conferences resist a one-hour talk about nothing? Didn’t anybody scream, try to activate the fire alarm, jump out of the window?

What makes matters worse is that I have seen good researchers referring to these results as a serious explanation of why quantum theory is not more non-local, at the same level of Information Causality or Non-Trivial Communication Complexity (see the Wikipedia entry that started this post).

That’s depressing, rats. Nobody in the community gave a damn about the article before it got published in Sci... the famous journal. The minute it got accepted, people started praising the “discovery” like the invention of penicillin, the cognitive schema being: “the paper appeared in _____, which is a sound journal. Therefore, the results are sound” [compare with: “Barbra Streisand plays hot women in movies. Therefore, she’s hot”].

So conference organizers, wikipedists, nonlocality researchers and book editors, this is my message to you: come on, guys. The article has three pages. It would have taken you ten minutes to read it critically and decide by yourselves that it was a piece of shit. Instead, you chose to inhibit all frontal lobe activity just because some editor of Tralala magazine had a weird day. Well, that is the past, and you cannot change it (I think). In the future, though, listen to your own criterion*.

Yours truly,

Schroedinger’s rat

*Your criterion is this little gentleman who lives inside your head and tells you: “this is good, that is bad”. He doesn’t work for Nature, Science or PNAS.