Spooky action put to order: Physicists classify different types of 'entanglement'

Jun 06, 2013

A property known as "entanglement" is a fundamental characteristic of quantum mechanics. Physicists and mathematicians at ETH Zurich show now how different forms of this phenomenon can be efficiently and systematically classified into categories. The method should help to fully exploit the potential of novel quantum technologies.

"I think I can safely say that nobody understands quantum mechanics." Thus spoke the American physicist Richard Feynman—underlining that even leading scientists struggle to develop an intuitive feeling for quantum mechanics. One reason for this is that often have no counterpart in classical physics. A typical example is the : seem to directly influence one another, no matter how widely separated they are. It looks as if the particles can 'communicate' with one another across arbitrary distances. , famously, called this seemingly paradoxical behaviour "spooky action at a distance."

When more than two particles are entangled, the mutual influence between them can come in different forms. These different manifestations of the entanglement phenomenon are not fully understood, and so far there exists no general method to systematically group entangled states into categories. Reporting in the journal Science, a group of mathematicians and physicists around Matthias Christandl, professor at the Institute for , provides an important contribution towards putting the "spooky action" to order. The team has developed a method that allows them to assigning a given quantum state to a class of possible entanglement states. Such a method is important because, among other things, it helps to predict how potentially useful the can be in technological applications.

Putting entangled states in their place

Together with Brent Doran, a professor in the Department for Mathematics at ETH Zurich, and David Gross, a professor at the University of Freiburg in Germany, Christandl and his PhD student Michael Walter, first author of the Science publication, introduce a method in which different classes of entangled states are associated with geometric objects known as polytopes. These objects represent the "space" that is available to the states of a particular entanglement class. Whether or not a given state belongs to a specific polytope can be determined by making a number of measurements on the individual particles. Importantly, there is no need to measure several particles simultaneously, as is necessary in other methods. The possibility to characterise entangled states through measurements on individual particles makes the new approach efficient, and means also that it can be extended to systems with several particles.

The ability to gain information about entangled states of several particles is a central aspect of this work, explains Christandl: "For three particles, there are two fundamentally different types of entanglement, one of which is generally considered more 'useful' than the other. For four particles, there is already an infinite number of ways to entangle the particles. And with every additional particle, the complexity of this situation gets even more complex." This quickly growing degree of complexity explains why, despite a large number of works that have been written on entangled states, only very few systems with more than a handful of particles have been fully characterized. "Our method of entanglement polytopes helps to tame this complexity by classifying the states into finitely many families," adds Michael Walter.

Quantum technologies on the horizon

Quantum systems with several are of interest because they could take an important role in future technologies. In recent years, scientists have proposed, and partly implemented, a wide variety of applications that use quantum-mechanical properties to do things that are outright impossible in the framework of classical physics. These applications range from the tap-proof transmission of messages, to efficient algorithms for solving computational problems, to tech-niques that improve the resolution of photolithographic methods. In these applications, are an essential resource, precisely because they embody a fundamental quantum-mechanical phenomenon with no counterpart in . When suitably used, these complex states can open up avenues to novel applications.

A perfect match

The link between quantum mechanical states and geometric shapes has something to offer not only to physicists, but also to mathematicians. According to Doran, the mathematical methods that have been developed for this project may be exploited in other areas of mathematics and physics, but also in theoretical computer science. "It usually makes pure mathematicians a bit uncomfortable if someone with an 'applied' problem wants to hit it with fancy mathematical machinery, because the fit of theory to problem is rarely good," says Doran. "Here it is perfect. The potential for long-term mutually beneficial feedback between pure mathematicians and quantum information theory and experiment is quite substantial."

The method of entanglement polytopes, however, is more than just an elegant mathematical construct. The researchers have shown in their calculations that the technique should work reliably under realistic experimental conditions, signalling that the new method can be used directly in those systems in which the novel are to be implemented. And such practical applications might eventually help to gain a better understand of .

Explore further: Simon's algorithm run on quantum computer for the first time—faster than on standard computer

More information: Walter M, Doran B, Gross D, Christandl M: Entanglement Polytopes: Multi-Particle Entanglement from single-particle information. Science, 2013.

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vacuum-mechanics
1 / 5 (12) Jun 06, 2013
"I think I can safely say that nobody understands quantum mechanics." Thus spoke the American physicist Richard Feynman—underlining that even leading scientists struggle to develop an intuitive feeling for quantum mechanics. One reason for this is that quantum phenomena often have no counterpart in classical physics…..

Nowadays, it seems that this is no longer being true! Maybe this physical working mechanism could help everybody understands quantum mechanics.
http://www.vacuum...19〈=en
ValeriaT
3.4 / 5 (5) Jun 06, 2013
alfie_null
5 / 5 (1) Jun 07, 2013
[Nowadays, it seems that this is no longer being true! Maybe this physical working mechanism could help everybody understands quantum mechanics.
http://www.vacuum...19〈=en

Yawn. Yes, we know - you want to evangelize your vacuum mechanics crankology. Been seeing lots of posts that are slight variations on this on phys.org physics topics. Your posts have no useful content and arguably should be considered as spam by the site administrators.
aroc91
1 / 5 (1) Jun 11, 2013
[Nowadays, it seems that this is no longer being true! Maybe this physical working mechanism could help everybody understands quantum mechanics.
http://www.vacuum...19〈=en

Yawn. Yes, we know - you want to evangelize your vacuum mechanics crankology. Been seeing lots of posts that are slight variations on this on phys.org physics topics. Your posts have no useful content and arguably should be considered as spam by the site administrators.


It's definitely spam, but admins/moderators here are few and far between. If they did their job, half the people here would have been banned years ago.
ValeriaT
1 / 5 (4) Jun 11, 2013
If they did their job, half the people here would have been banned years ago.
The callers for censorship should be banned first. But I've to admit, I don't see any contribution in spewing of the same link again and again outside of any context and without willingness to some discussion about. What this forum is actually lacking is the possibility to place certain posters to private black list, which would filter out their comments at personal basis (i.e. without interfering of the other readers, who can have different opinion about it). This is the only democratic way of "censorship", which I could support.
aroc91
not rated yet Jun 12, 2013
The callers for censorship should be banned first


Over omatumr's iron sun, Pirouette's transparent Martian creature, and Vendicar's completely off topic political nonsense? The rules are very clear.

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