RECENT ARTICLES

To build the ultimate artificial mimics of real life systems, we may need to use quantum memory.

A radical interpretation of physics makes quantum theory more personal.

Carlo Rovelli describes how black holes may transition to "white holes," according to loop quantum gravity, a radical rewrite of fundamental physics.

Could giant sea swells help explain how the macroscopic world emerges from the quantum microworld? (Image credit: MIT News)

A "retrocausal" rewrite of physics, in which influences from the future can affect the past, could solve some quantum quandaries—saving Einstein's view of reality along the way.

FQXI ARTICLE

February 26, 2017

Discord in the Quantum World

An alternative quantum resource to entanglement could help physicists in the quest to construct a quantum computer.

May 22, 2013

Wojciech Zurek

Los Alamos National Laboratory

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?

Major progress on the understanding

of the quantumness of correlations

this long after quantum theory

was developed is exciting.

of the quantumness of correlations

this long after quantum theory

was developed is exciting.

- Wojciech Zurek

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

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.

Vlatko Vedral

University of Oxford

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.

Discord would make the

realization of quantum

advantages a lot more

tractable.

realization of quantum

advantages a lot more

tractable.

- Animesh Datta

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,

Animesh Datta

University of Oxford

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."

Comment on this Article

Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!

function ValidatePostText_main () {
form = document.addPostForm_main;
if (form.postText_main.value == '') {
alert ("The post contains no text");
return false;
}
else {
return true;
}
}

**Your name:**
(optional)

**Important:** In order to combat spam, please select the letter in this menu between 'J' and 'L':
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z

Recent Comments

read all article comments

Please read the important Introduction that governs your participation in this community. Inappropriate language will not be tolerated and posts containing such language will be deleted. Otherwise, this is a free speech Forum and all are welcome!

Please enter the text of your post, then click the "Submit New Post" button below. You may also optionally add file attachments below before submitting your edits.

HTML tags are not permitted in posts, and will automatically be stripped out. Links to other web sites are permitted. For instructions on how to add links, please read the link help page.

You may use superscript (10

^{100}) and subscript (A_{2}) using [sup]...[/sup] and [sub]...[/sub] tags.You may use bold (

**important**) and italics (*emphasize*) using [b]...[/b] and [i]...[/i] tags.You may also include LateX equations into your post.

Insert LaTeX Equation
[hide]

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation

clear equation

insert equation into post at cursor

LaTeX equations may be displayed in FQXi Forum posts by including them within [equation]...[/equation] tags. You may type your equation directly into your post, or use the LaTeX Equation Preview feature below to see how your equation will render (this is recommended).

For more help on LaTeX, please see the LaTeX Project Home Page.

LaTeX Equation Preview

preview equation

clear equation

insert equation into post at cursor

Attachments
[hide]

You may optionally attach up to two documents to your post. To add an attachment, use the following feature to browse your computer and select the file to attach. The maximum file size for attachments is 1MB.

Once you're done adding file attachments, click the "Submit New Post" button to add your post.

You may optionally attach up to two documents to your post. To add an attachment, use the following feature to browse your computer and select the file to attach. The maximum file size for attachments is 1MB.

Once you're done adding file attachments, click the "Submit New Post" button to add your post.

PETER JACKSON wrote on July 4, 2014

Han,

"the setting parameters are averages of the probability densities." Or indeed the converse. I've agreed in my recent essay (see in 'Contests');

Do Bob and Alice have a future? which describes a way of deriving QM's predictions and nonlocality geometrically.

Good to see you here but your equations don't appear, and this has long been dead. Perhaps better to re-post on "Why Quantum..."

I'd also be glad for you to take a look at and comment on my 2 page summary...

Han,

"the setting parameters are averages of the probability densities." Or indeed the converse. I've agreed in my recent essay (see in 'Contests');

Do Bob and Alice have a future? which describes a way of deriving QM's predictions and nonlocality geometrically.

Good to see you here but your equations don't appear, and this has long been dead. Perhaps better to re-post on "Why Quantum..."

I'd also be glad for you to take a look at and comment on my 2 page summary...

HAN GEURDES wrote on July 4, 2014

Dear all,

Suppose, [equation] .

Then, [equation] .

Hence, [equation] .

Now, [equation] .

Hence, [equation] and so, we may define

[equation] and [equation] with

[equation]

It can be demonstrated that there are [equation] such that [equation] and [equation] .

Hence, a Bell form,

[equation] has been found.

So LHV are not impossible when we consider that the setting parameters are averages of the...

Dear all,

Suppose, [equation] .

Then, [equation] .

Hence, [equation] .

Now, [equation] .

Hence, [equation] and so, we may define

[equation] and [equation] with

[equation]

It can be demonstrated that there are [equation] such that [equation] and [equation] .

Hence, a Bell form,

[equation] has been found.

So LHV are not impossible when we consider that the setting parameters are averages of the...

DR. EDWARD SIEGEL wrote on November 6, 2013

MUCH-HYPED TRENDY "QUANTUM-COMPUTING" IS ALIVE AND WELL AND IN ANN AI HAS BEEN FOR SOME 34 YEARS NOW!!!

EDWARD SIEGEL(1980)WITH CHARLES ROSEN(RIP)CEO OF MACHINE-INTELLIGENCE(ATHERTON, CA)AND CALTECH CONSULTANT RICHARD FEYNMAN(RIP)AND VESKO MARINOV AND ADOLPH SMITH OF EXXON ENTERPRISES/A.I. AND H.P.'S IRWIN WUNDERMAN(RIP)[THE INVENTOR OF THE CALCULATOR]

(1) EUREKA: TRIVIALLY NOTICED THAT IN ARTIFICIAL NEURAL-NETWORKS(ANN) ARTIFICIAL-INTELLIGNCE(A.I.) THE BY-ROTE ON-NODE SWITCHING...

MUCH-HYPED TRENDY "QUANTUM-COMPUTING" IS ALIVE AND WELL AND IN ANN AI HAS BEEN FOR SOME 34 YEARS NOW!!!

EDWARD SIEGEL(1980)WITH CHARLES ROSEN(RIP)CEO OF MACHINE-INTELLIGENCE(ATHERTON, CA)AND CALTECH CONSULTANT RICHARD FEYNMAN(RIP)AND VESKO MARINOV AND ADOLPH SMITH OF EXXON ENTERPRISES/A.I. AND H.P.'S IRWIN WUNDERMAN(RIP)[THE INVENTOR OF THE CALCULATOR]

(1) EUREKA: TRIVIALLY NOTICED THAT IN ARTIFICIAL NEURAL-NETWORKS(ANN) ARTIFICIAL-INTELLIGNCE(A.I.) THE BY-ROTE ON-NODE SWITCHING...

read all article comments

And select the letter between 'W' and 'Y':