Well, the rat is out of the bag; Schroedinger’s Rat, that is. That’s the new quantum blog by Miguel Navascues and boy is it snarky! I was keeping it under my hat for a while so I could enjoy it privately, but the time has come to announce it to the world. Miguel is fearless about shouting his colorful opinions from the rooftops, and I can respect that, even if I don’t agree with everything he says.

Miguel’s second post is all about quantum discord. As anyone who reads quant-ph knows, there are around two or three papers per week about discord for years now. Unfortunately, a huge number of these are nearly worthless! Quoth the Rat:

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…

If you thought he was exaggerating, here is a paper that has been cited 263 times since May 2009: Robustness of quantum discord to sudden death. Wow, discord is immortal! And in case you want more, you can just go to quantumdiscord.org and find a list of discord papers and see for yourself.

Before we can treat the patient we have to understand the disease, and this is exemplified by a typically test case: Quantum discord for two-qubit X-states (cited 256 times). The authors compute the quantum discord and a few other entanglement measures for a family of two-qubit states and conclude that there is no obvious relationship between the various measures. Why did they do this? “Because it’s there” might have been a good reason to scale Everest, but this feels more like a homework assignment for a graduate course. Wait, I take that back: Scott’s students’ homework is much more interesting and relevant.

*But Steve! What about all the ***good*** discord papers? You can’t just trash the entire field! *

You’re absolutely right, there *are* good discord papers. I can even name about 5 of them, and I’m willing to bet there are as many as 12 or 15 total. My intention is definitely not to trash the subject as *intrinsically* uninteresting; rather, I want to highlight the epidemic of pointless papers that constitute the discord bubble. I hope that thinning the herd will increase the quality of the results in the field and decrease the hype surrounding it, because it has really gotten completely out of control.

Here are some good rules of thumb for those moments when you find yourself writing a discord paper. If you are calculating something and you don’t know why you are calculating it, then close your latex editor. You do not have one of the good discord papers. If the discord you calculated is not related to a resource (physical, computational, etc.) in a quantifiable way, you probably don’t have a good discord paper. If it *is* related to a resource, but you had to concoct that relationship in a totally ad hoc way that doesn’t generalize, then you do not have a good discord paper. Ditto if the relationship is via a protocol that literally nobody cares about. If you only have two qubits, you almost certainly don’t have a good discord paper. Good theory papers usually have $latex n$ qubits. And if your weak theory result suffers from one or more of the above but you add in some equally unimpressive experimental results to cover up that fact, then you absolutely, unequivocally do not have a good discord paper. I don’t care what journal it’s published in, it is not a good paper and you should be ashamed of yourself for inflating the bubble even further.

As bad as the authors are, this bubble is also the fault of the referees. *Simply being correct is not enough to warrant publication.* It also has to be new, non-trivial, and interesting. Please referees, “Just Say No” to papers that don’t meet this standard!

Enough of this bad medicine. In the comments, feel free to mention some of the *actually good* discord papers, and why they deserve to keep their value after the bubble bursts.

I feel I need to comment on this post, mainly because there is a lot of truth in it. However some historical perspective may help justify some work on discord. Discord was defined by Zurek in relation to decoherence. This relation to decoherence is still being studied and discord is indeed a useful quantity in Zurek’s program of Quantum Darwinism. (see arXiv:1112.6238 sec VII.A for a review on discord in this context). The “classical correlations” (mutual information minus discord) were defined from a more information theoretic perspective by Hendersond and Vedral. There are a number of uses for this quantity, most notably in relation to locally accessible information and purification, as in the Koashi-winter relation. So at least historically the idea of discord was motivated by a little more then a discrepancy between two definitions for mutual information.

The discord “boom” started following a number of results. 1. The relation between discord and Completely positive dynamics. 2. The similarity between discord and the

information or quantum deficit (see arXiv:1112.6238 II.B and VII.C). 3. The result regarding discord in DQC1.

I will skip 1. since results along those lines are problematic at best and did not get followed by anything significant. The other two are related to issues concerning quantum correlations in mixed states.

Entanglement is not well defined in mixed states. The various definitions are usually in the context of a resource for LOCC. This does not account for all phenomena we expect to be related to correlations and LOCC. This last observation is the idea behind the quantum deficit. In the context of LOCC the quantum deficit is quite an important idea, it points to the difference between doing things with LOCC and doing them with non-local operations.

The result involving quantum computation was probably the biggest catalyst for discord research. And probably for the wrong reasons. Although the result of Datta

Shaji and Caves (DSC) was very good their interpretation was taken too far. Again we need some perspective. In pure state quantum computation it is well known that

entanglement is necessary for significant speed-up. In mixed state quantum computation it is clear that correlations play a role in the speed-up, but it is not clear

if entanglement is necessary. DSC’s result suggested that discord plays the same role in mixed state quantum computing as entanglement in pure states. This result is

very significant. However I think that some people took it too far, that is, they suddenly decided to treat discord in mixed states in the same way as entanglement in

pure states. Now, unlike entanglement, discord is not a resource under a known class of operations. For example it can increase under local operations. Papers treating or “selling” discord as a resource are perhaps the main reason for the controversy around discord research. However there are other interesting lines of research related to discord, and similar quantities. I think (hope) mine is among these.

Thanks for the detailed comment! Regarding the Datta-Shaji-Caves paper, I think you are right that it is an interesting result; it’s one of the good discord papers that I had in mind. I looked at their paper again before writing this post, and it seemed clear to me that the claim of [discord > 0] => [reason for mixed state speedup] was already understood to be speculative at the time. (Go read the last paragraph… it would be hard to characterize it as hype.) Moreover, there is entanglement between all the other bipartitions in a generic DQC1 circuit, which is something that rarely gets mentioned.

What I don’t understand is how the speculative and weak evidence that “discord explains the power of mixed-state quantum computation” became a license to print money, or rather bad papers. It clearly wasn’t the intention of the authors to start that avalanche, but it happened anyway.

I actually appreciate the attempts to use discord as a resource. At least those papers make an effort to be interesting, even though it is often a tenuous or dubious connection to an uninteresting protocol. The ones that really annoy me are the ones where they simply compute the discord for some particular state or family of states for essentially no reason.

I should correct myself. The attempts to identify discord as a resource is not the problem in itself. But it causes the problem of people treating discord as a resource in the same way as entanglement. Eg. showing there is a lot of discord in this and that system, discord behaves better then entanglement etc..

By the way, I very much like your rules of thumb 🙂

“Entanglement is not well defined in mixed states. The various definitions are usually in the context of a resource for LOCC. This does not account for all phenomena we expect to be related to correlations and LOCC. ”

I don’t understand what you are talking about. Can you elaborate?

Entanglement is not well defined in mixed states: There is no unique measure of entanglement, even in the bipartite case. Moreover measures like entanglement of distillation vanish for non-separable (bound entangled) states.

There is also another issue of entanglement vanishing at a very strange point when noise is added. For example the 1/3 mark for Werner states which seems a bit bizarre.

The various definitions are usually in the context of a resource for LOCC: This is the starting point for the definitions of entanglement monotones. i.e non-increasing under LOCC. The general definition of separable vs entangled can also be described in terms of LOCC. e.g “Entanglement cannot be created under LOCC”.

This does not account for all phenomena we expect to be related to correlations and LOCC: One example is mixed state quantum computation where the quantum speed-up may exist even when entanglement is vanishingly small. In DQC1 as calculated in arXiv:quant-ph/0505213 (Datta, Flammia, Caves). There are also other examples, the most prominent being “Quantum Nonlocality without Entanglement” arXiv:quant-ph/9804053 but also the quantum deficit. In these cases non-local strategies can be used to outperform local ones even in the case where there is no entanglement in the input-output states.

“Entanglement is not well defined in mixed states: There is no unique measure of entanglement, even in the bipartite case. ”

Wrong. For example, squashed entanglement is well defined and it vanishes iff the state is separable. Is squashed entanglement unique? Don’t know what you mean by that. Each element in a set is considered unique. Uniqueness depends on how you define your set and the elements in it. You haven’t done that for entanglement measures. Is discord unique, according to your definition?

The rest of your comments are just as illogical.

Slightly off-topic, but please let me commend Gil Kalai’s present topic “

Symplectic Geometry, Quantization, and Quantum Noise“.It’s troubling that snarky critiques of “not even wrong” articles are prominent in public quantum discourse … perhaps non-snarky quantum weblogs like Gil’s are worthy of mention and a comparable share of comments?

I guess the reason for the snark/negativity is a response to what Schrodinger’s Rat complains about which is that everyone is always polite and positive about everything publicly, while having their likes and dislikes in private. However, this can lead to a misleading public perception of what most researchers think.

Quantum Discord Creationists

Quantum Discord Zombie Hordes

Hi Steve,

thanks for your post, in particular for highlighting how there are some good works out there that deserve to survive the collapse of the bubble. This is something that was missing in Miguel’s original post. Please find a short list—with some self-advertisement, I am afraid—below (BTW: what is your list?).

I agree most of your post. The only remark I feel like making at the moment is that some of the fundamental papers in quantum information deal with two qubits: “playing” with the simplest case is often very illuminating/useful. So I tend to consider the rule of thumb “If you only have two qubits, you almost certainly donâ€™t have a good discord paper” as a bit too strong 🙂

Ciao,

Marco

%%%%%%%%%

Some works that I think — or rather hope, in the case of my own papers 🙂 — have some lasting values are (the list is incomplete):

Marco Piani, PaweÅ‚ Horodecki, and Ryszard Horodecki

“No-Local-Broadcasting Theorem for Multipartite Quantum Correlations”

http://prl.aps.org/abstract/PRL/v100/i9/e090502

In that paper we cast/generalize one of the basic features of quantum information — no-cloning/no-broadcasting — purely in terms of correlations

The connection with the standard no-broacasting theorem was made clearer by Luo and collaborators, in particular finally clarified in

Shunlong Luo and Wei Sun

“Decomposition of bipartite states with applications to quantum no-broadcasting theorems”

Phys. Rev. A 82, 012338 (2010)

The role of the general quantumness of correlations in the measurement process was highlighted in

Alexander Streltsov, Hermann Kampermann, Dagmar BruÃŸ

“Linking Quantum Discord to Entanglement in a Measurement”

http://arxiv.org/abs/1012.4903

We obtained essentially the same result, although starting from a different point of view — that is trying to relate the quantumness of correlations with relatively well-established notions of non-classicality in quantum optics

Marco Piani, Sevag Gharibian, Gerardo Adesso, John Calsamiglia, Pawel Horodecki, Andreas Winter

“All non-classical correlations can be activated into distillable entanglement”

http://arxiv.org/abs/1103.4032

We later proved a general hierarchy between entanglement and general quantumness of correlations based on the framework of the previous two papers

Marco Piani, Gerardo Adesso

“The quantumness of correlations revealed in local measurements exceeds entanglement”

http://arxiv.org/abs/1110.2530

In particular we point out that in the simplest instances — no noise, no decoherence — of von Neumann chains (the kind of chain of interactions between physical systems involved in the measurement process first considered by von Neumann) entanglement never decreases along the chain.

General results about the relation between decoherence and quantumness of correlations were obtained by Patrick Coles, in particular in

Patrick Coles

“Unification of different views of decoherence and discord”

http://arxiv.org/abs/1110.1664

B. Eastin proved in

B. Eastin

“Simulating Concordant Computations”

http://arxiv.org/abs/1006.4402

that in a precise, technical, and somewhat restricted sense, discord is needed to have a quantum speed-up in quantum computation

G. Adesso and collaborators pointed out how the uncertainty in measuring a local observable is linked to the general quantumness of correlations:

Davide Girolami, Tommaso Tufarelli, Gerardo Adesso

“Quantum uncertainty on a single observable”

http://arxiv.org/abs/1212.2214

I have not gone through the details yet, but my feeling is that they highlight a key feature of (general) quantum correlations.

Also (this is a kind of review of previous work by the same authors, with some new results)

M. Horodecki et al.

“Local versus non-local information in quantum information theory: formalism and phenomena”

http://arxiv.org/abs/quant-ph/0410090

From the abstract: “In general the information is a mixture of local, and non-local (“quantum”) information. To make this point more clear, we develop and investigate the quantum information processing paradigm in which parties sharing a multipartite state distill local information.”

I think the views expressed on quantum discord bubble is too strong. You do not expect breakthroughs everyday. Science makes progress step by step little by little. Who are you to judge what is a bad or a good paper. Only time will tell what is important and what is not. I think this kind of personal views should be banned on any scientific forum.