# Order from Quantum Discord

Have they no shame?
Even our children are already indoctrinated by popular Disney cartoons to think that Discord is bad. Borivoje Dakić et al. beg to differ.

Conventional hardware thrives on our ability to create precision structures in the micro domain.  Computers are highly ordered and usually (for good reason) regarded as perfectly deterministic in the way that they process information. After all, the error rate of the modern computer is astronomically low.

Even before the advent of quantum computing, it was discovered that this defining feature of our hardware can sometimes be a disadvantage i.e. randomized algorithms can sometimes outperform deterministic ones. Computers actually gain functionality by being able to use randomness as an information processing resource.

Due to their fundamentally probabilistic nature, randomness is always inherent in quantum computing designs. On the other hand, most quantum computing algorithms exploit one of the most fragile, ordered physical states: Entanglement, the peculiar quantum mechanical phenomenon that two systems can be entwined in a common quantum state. It is characterized by perfect correlation of spatially or temporally separated measurements.  The simplest protocol to exploit this feature is the quantum information channel, and it results in some quite surprising and, as is so often the case with quantum mechanics, counter-intuitive results. For instance, if two parties are connected via two very noisy directional channels with zero quantum information capacity, the participants will still be able to establish a qubit flow via entanglement distillation.

It has often been argued that entanglement is at the heart of quantum computing.  This credo has caused quite a bit of grief for the company D-Wave, that lays claim on shipping the first commercially available quantum computer. Although their erstwhile fiercest critic Scot Aaronson has made peace with them, he expressed that he still would like to see a measure for the degree of entanglement that they achieve on their chip.

Is it therefore quite surprising to see papers like this one recently published in Nature Physics that describe Quantum Discord as an optimal resource for quantum information processing. On first glance, some of this seems to be due to semantics.  For instance, John Preskill refers in his overview paper to all non-classical correlations as entanglement, but strictly speaking the term entanglement would never be applied to separable states. However, the paper demonstrates, theoretically as well as experimentally, that separable two qubit states with non-vanishing quantum discord can be found that offer better performance for their test case of quantum teleportation than a fully entangled state:

Experimentally achieved Remote State Preparation payoff for 58 distinct states of a Bloch sphere. Shown are the respective values for the two resource states $\tilde{p}_w$(red) and $\tilde{p}_B$ (blue). The dashed lines represent the theoretical expectations. There is a clear separation between the two resource states, which indicates that the separable state $\tilde{p}_w$ is a better resource for RSP than the entangled state $\tilde{p}_B$.

This raises the exciting prospect of a new approach to quantum computing that may not require the notoriously difficult preservation of entangled states,  giving hope that there may yet be a viable approach to quantum computing for the rest of us without requiring helium cooling infrastructure. Subsequently, quantum discord has become a research hot topic that spawned a dedicated site that helps keep track of the publications in this area.

At this point it is not obvious (at least to me) what impact these new insights on quantum discord will have in the long run, i.e. how do you develop algorithms to take advantage of this resource, and how will it, for instance, impact the channel capacity for quantum communication? (For a take on the latter see R.Tucci's latest papers).

What seems clear, though, is that D-Wave has one more good argument to stress the inherent quantumness of their device.

There is a really poorly produced video lecture available on this subject by a co-author of the Quantum Discord paper. (If only the presenter stopped moving so that the camera would not have to be constantly and noisily adjusted). Possibly the point of this dismal production value is to illustrate headache-inducing discord. In that case the University of Oxford certainly succeeded spectacularly.

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### 2 Responses to Order from Quantum Discord

1. Henning, for me the real problem is that after 20 years of quantum computing research, we still don’t have a single example of a quantum algorithm that achieves any asymptotic speedup whatsoever — even a polynomial speedup, even conjecturally — using separable mixed states only. It’s true that we also don’t have a proof that there are no such speedups, but it seems like a plausible conjecture. More important, even if that conjecture turned out to be false, any hypothetical speedup using separable mixed states would still require 2-qubit gates, of the sort that could very easily also be used to prepare entangled states. So in some sense, the fact that entanglement was never generated in this particular computation would just be a mathematical curiosity: the computation still required entangling operations! So I think the question of whether D-Wave can entangle its qubits remains as pertinent as it ever was.

Speaking of which, I found a couple statements in the new Nature Physics paper (which I hadn’t seen, thanks!) to be a little misleading. As I said, we don’t know how to solve any problem thought to be classically intractable without generating entanglement. The authors discuss the DQC1 model, but contrary to what they say, that model does produce some entanglement. The issue is just that, according to physicists’ standard entanglement measures, it looks like a “tiny amount” of entanglement. But in the sense relevant to computational complexity, it could easily be that “a little entanglement (as produced by DQC1) goes a long way,” and is drastically different from no entanglement!

2. Henning Dekant says:

Scott, thank you for this insightful comment, this adds some balance to the Nature Physics paper. When I first learned about Quantum Discord I thought it was just entanglement repackaged. At this point I convinced myself that it makes for a good measure of quantumness, but the claim that this paper makes with regards to separable states certainly came as a surprise to me. Given the reputation of the journal as well as the universities and institutes involved it certainly scored high on my truthiness scale. And then there are other papers piling on, selling us on the notion that this new kid on the blog beats out entanglement. On the other hand this talk and paper very much illustrate your point.

While loving the science I also try to cover the emerging QC business side. At this point this pretty much means D-Wave. To the extent that this muddies the waters it helps their claim to have the first quantum computing device on the market.

A better understanding of the entanglement on their RAINER chip would be very interesting but I don’t think it necessarily makes for a good cost/benefit ratio.