Discord in the Quantum World

As Heisenberg famously noted, in the quantum world, no matter how hard you try to scrutinise a system, you will always be left in the dark about some of its aspects. The same appears to be true on a sociological level—at least in the burgeoning research area investigating a property of quantum systems known as discord. The discord of a system mathematically quantifies how much it is disrupted when measured. Over the past five years, this obscure measure has been generating excitement as an alternate resource that could drive the search for sustainable quantum computation. If true, quantum computers could be easier to build than had been thought.

But as more energy—both theoretical and experimental—has been devoted to examining these claims, the more confused the consensus is becoming about discord’s potential: Is quantum discord the solution to realistic quantum computing, as some have argued? Or has the whole area become a bubble —that’s about to burst?

The current debate is testament to the huge impact that quantum discord is having on the scientific landscape. The quantity was first defined by FQXi member Wojciech Zurek, a physicist at the Los Alamos National Laboratory in New Mexico, at the turn of the century. Zurek was not thinking about quantum computing in particular; rather, he was trying to get a better handle on what "quantumness" is. In the quantum world, strange things can happen: particles can be here and there at the same time, and can maintain spooky connections with others across time and space. But we do not encounter these peculiarities in everyday life. What, Zurek pondered, is the essential property that distinguishes the weird fuzzy, behaviour at the sub-microscopic world from the macroscopic, classical world we see around us?

A key feature of the quantum world is that particles can exhibit correlations that have no counterpart in our everyday world and cannot be described by standard probabilities. They seem to know more about each other and in ways that are more intimate than is possible in the classical world. In particular, the mysterious phenomenon of entanglement has long fascinated physicists. Famously dubbed "spooky action at a distance" by Einstein, multiple quantum particles, such as photons, can be prepared in such a way that they behave as one when measured. This troubled Einstein because the outcome of different measurements should be random and unconnected. But the binding holds regardless of how far apart the partners are, as though the particles are communicating the results of their measurements to each other, faster than the speed of light.

Entanglement has been verified many times in the laboratory, by measuring the properties of pairs of twinned particles and confirming that they match up to a greater degree than can be explained by classical physics. This behaviour is driven by another quantum oddity: Prior to observation, quantum systems do not exist in one set state; instead they exist as a multiplicity of states simultaneously. The mere act of measurement forces the system to choose a single state of being, instantaneously altering all the particles it encapsulates, no matter how far apart they are from each other.

By the 1980s, physicists realised that this quantum weirdness could be used to create computers with capabilities that are magnitudes more powerful than those we have today. Rather than simply encoding information classically in bits that can take values of 0 and 1, quantum computers would manipulate so-called qubits that exist as both 0 and 1 simultaneously. Entanglement was considered to be integral to the power of any quantum computer because it would tie together multiple qubits, allow calculations to be carried out across them in parallel, at unimaginably high speeds. In the 1990s, algorithms were developed that would, in theory, employ entanglement to factorize large numbers, or search databases at super-fast speeds, for instance.

Zurek’s instinct, however, was that while entanglement is a hugely important quantum property—with potential practical applications—alone it does not fully express what quantumness is. He had spent many years musing over exactly how the transition from the quantum to the classical world unfolds through a process called decoherence. What he realised, through mathematical analysis, was that entanglement could not be the full story regarding quantum correlations because even when entanglement disappears from a system, decoherence is not yet done in its task of making systems classical. Even in this halfway state, he calculated, the system will be disturbed by measurements—a quintessentially quantum feature.

Mutual Information

In 2000, Zurek used two classical measures of how much two systems know about each other—known as "mutual information"—to define a quantity that he called quantum discord. The two formulae for mutual information coincide when there is an underlying probability distribution that can describe the state of the two correlated systems. Zurek realized that, in a quantum world, this is not the case, and so the two formulae are no longer identical. The quantum discord is given by the difference between them. With the help of one of his students, Harold Ollivier, Zurek related this new quantity to decoherence.

Other physicists were also moving towards the conclusion that a new quantity was needed to fully appreciate the meaning of quantumness. Physicists Vlatko Vedral and Leah Henderson, both at the University of Oxford, UK, independently discovered that quantum discord must exist, in 2001. They were trying to sum up the correlations in a system, which much have both classical and quantum contributions. At first, they assumed the latter component could be completely identified with entanglement. "When you subtract classical correlations from total correlations in a quantum state, you would expect that the result ought to be entanglement," Vedral explains. To his surprise, however, there was another unidentified quantity messing up that simple equation. Once more, the missing mathematical piece was discord. "This is how discord was born," Vedral recalls.

To understand this strange discrepancy in the correlations, physicists had to remember that we do not live in a perfect world. Under ideal conditions, quantum states are termed "pure" and entanglement is the only type of weird quantum correlation that exists between them. But in the real world, many systems are messy: they contain both quantum particles and intrusion from their environment —in the form of thermal disturbances, for instance—leading the quantum states to become "mixed" with elements of classical probability. In mixed states, Zurek’s and Vedral’s calculations showed, some quantum correlations continue to exist after entanglement is destroyed, and these additional interactions are mathematically expressed by the system’s discord.

At that time, for Zurek, Ollivier, Vedral and Henderson, discord was interesting for theoretical reasons because it redefined and broadened the notion of what was a quantum correlation. "The fact that there was a major progress on the understanding of the quantumness of correlations this long after quantum theory was developed is exciting," Zurek says. Even so, quantum discord initially produced only a trickle of related papers examining this intriguing but abstract concept.

But in recent years, the concept of discord has gained significant—and unexpected—popularity as a potential solution to solving the practical problems of making quantum computers work. Currently, the physical systems able to store pure qubits, even for a few milliseconds, are exotic, such as extra-cold atoms. Entanglement between these qubits is difficult to create and maintain, so the reliance on entanglement as a mechanism for quantum computing means that systems require careful preparation and are highly fragile. A permanent solution, similar to modern computer processors and hard drives, still seems a long way off.

Discord, by contrast, is more robust than entanglement, and far less likely to be destroyed by thermal noise in the lab. The question is, can it be usefully harnessed to power superfast computations? In 2008, it suddenly seemed that the answer was "yes"—thanks to a theoretical analysis carried out by quantum physicists Animesh Datta, Carlton Caves and Anil Shaji, then at the University of New Mexico.

Power of One Qubit

The catalyst was linking discord to a puzzling stylized model for quantum computation called the "power of one qubit"—or DQC1, for short. Rather than attempting to entangle many pure qubits together, here, a pure qubit is coupled to a set of mixed qubits—which can tolerate thermal noise. Together they are used to perform simple quantum computations. The system contains little or no entanglement because messy mixed states simply cannot support entanglement in the way that pure qubits can. But theoretically, the proposed model provides an exponential advantage over the best classical formulations for certain mathematical problems.

Such a computation to find the trace of a matrix, which essentially involves adding up certain numbers in a table, was carried out in the lab by Andrew White’s group at the University of Queensland, in Brisbane, Australia, in 2008. This was a proof-of-principle demonstration showing that the calculation could be done, but it did not attempt to achieve a super-fast speed up over a classical computation.

This demonstration seemed to hint that it may be far easier than first thought to build a robust quantum computer. Instead of having to string together a host of entangled pure qubits, experimenters would only need to control one single pure qubit. Datta notes, however, that there is still no formal proof that discord is behind DQC1. But if it is not discord that it powering the computation, it is not clear what else is doing this. It is also important to remember that the algorithms required to perform other tasks that have famously been linked to quantum computing, such as quickly searching through databases, or factorizing large numbers, still rely on entanglement. As yet, no discord-based algorithms for these purposes have been put forward.

Nonetheless, the practical implications of the DQC1 demonstration appeared to be huge. "Discord would make the realization of quantum advantages a lot more tractable, since discord is easier to generate and maintain, while entanglement is a very fragile resource," says Datta, now at the University of Oxford.

The popularity of this new concept has exploded in the last few years. Based on Google Scholar, Zurek estimates that 70-80% of all papers investigating and using discord were written in or after 2011, many of them inspired by the possible connection to quantum computing. Last year, Vedral organized an international conference on discord in Singapore that had close to 100 participants. Today, two to three papers a week are posted on the topic to the online Los Alamos archive, reflecting the growing body of interest.

Last year, Datta and Vaibhav Madhok at the University of New Mexico, showed that discord is an important theoretical quantity in the performance of a whole host of quantum communication protocols, as it captures the limitations and damaging effects of a noisy environment (V. Madhok & A. Datta, International Journal of Modern Physics B, 27, 1245041 (2013)). Vedral and a team of international collaborators also recently published results of an experiment showing that quantum advantages can be obtained in the absence of entanglement using only discord. Using laser pulses as carriers of information, the team encoded information into one pulse that was correlated to another one. The system was engineered so that the two pulses were not entangled in any way and the task was to retrieve the encoded information. To their delight, the team found that the two pulses were able to exchange information, despite the lack of entanglement. The amount of discord in the system acting as a guide as to how much information could be retrieved (M. Gu et al, Nature Physics 8, 671 (2012) and B. Dakic et al. Nature Physics 8, 666 (2012)).

The results highlight discord’s appeal. Experimentally, in the absence of entanglement, quantum discord is an achievable half-way house that confers some quantum advantages and may result in far superior performance than our everyday classical computers. "A discord-based mechanism would probably not be able to provide the maximum possible quantum advantage, but then no realistic device can," says Datta. "Both theoretically and experimentally, we have shown that discord is an important quantity."

But this rapid surge in interest about discord has also led to criticisms that the whole field has become a bubble. There are some good papers, such as those by Datta, Vedral and colleagues, and other independent researchers. But, unfortunately, there are also lots of low quality papers being pumped out that add little to our understanding of this new phenomenon, says Steve Flammia, an expert in quantum information theory at the University of Sydney. "Discord is certainly deserving of further work and shows promise, but it is still a long way away from being proven as the key to quantum computing," he cautions. Flammia is skeptical of the hype and worries that over-inflated expectations will lead to disappointment, so it is best to be realistic.

Additionally, a deluge of poor papers could damage the whole field. A similar bubble has been witnessed in the past, in other related quantum fields, including entanglement and quantum computing. The danger is that people will start to lose interest and miss potentially key findings, hidden in the masses of new papers.

For Zurek, the bubble says more about human nature and the competitive pressures of the academic world than about discord, in particular. "To begin with, quantum computing and information has become a bit of a bandwagon, which then led to the research on entanglement becoming a bit of a bandwagon when it looked like that was the key ingredient," he points out. This, "in turn led to the recent threat of discord becoming a bandwagon," he adds.

The temptation has also been to draw unhelpful and fictitious battle lines between entanglement and discord as the best way forward for building a quantum computer. But this runs counter to the intention of leading researchers, such as Datta and Vedral, who view discord as not as a rival to entanglement, but as a complement to it.

Marco Piani, a researcher on entanglement and other non-classical aspects of quantum correlations at the University of Waterloo, in Canada, believes too much effort is being spent at this stage on less helpful work, such as calculating the discord in all sorts of model systems. Instead, he argues that to mitigate the backlash, quantum physicists should focus on reaching the best possible understanding of what discord is, both from a fundamental point of view and for the sake of potential applications. That will help provide more evidence that studying these quantum correlations is justified and will even aid in understanding entanglement itself better.

"The future challenge is to develop a clearer understanding of quantum discord itself," agrees Datta. "A lot more is known about the behaviour of entanglement than discord, and we don’t know the half of what discord can be useful for."