Home > Press > Spooky action put to order Different types of 'entanglement' classified

Researchers at ETH Zurich have developed a method of assigning classes of complex quantum states to geometric objects known as polytopes.
Image: Amanda Eisenhut / ETH Zurich 
Abstract:
"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. A typical example is the quantum entanglement: Entangled particles 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. Albert Einstein, famously, called this seemingly paradoxical behaviour "spooky action at a distance."
Spooky action put to order Different types of 'entanglement' classified
Zurich, Switzerland  Posted on June 6th, 2013
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 Theoretical Physics, 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 quantum state 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 particles 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 quantummechanical properties to do things that are outright impossible in the framework of classical physics. These applications range from the tapproof transmission of messages, to efficient algorithms for solving computational problems, to techniques that improve the resolution of photolithographic methods. In these applications, entangled states are an essential resource, precisely because they embody a fundamental quantummechanical phenomenon with no counterpart in classical physics. 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 longterm 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 quantum technologies are to be implemented. And such practical applications might eventually help to gain a better understand of quantum mechanics.
Reference
Walter M, Doran B, Gross D, Christandl M: Entanglement Polytopes: MultiParticle Entanglement from singleparticle information. Science, 2013
####
For more information, please click here
Contacts:
Matthias Christandl
41446332592
Copyright © ETH Zurich
If you have a comment, please
Contact us.
Issuers of news releases, not 7th Wave, Inc. or Nanotechnology Now, are solely responsible for the accuracy of the content.
Bookmark:
News and information
Advantest to Exhibit at SEMICON Korea in Seoul, South Korea February 46 Showcasing Broad Portfolio of Semiconductor Products, Technologies and Solutions January 29th, 2015
Park Systems Announces Innovations in Bio Cell Analysis with the Launch of Park NXBio, the only 3in1 Imaging Nanoscale Tool Available for Life Science Researchers January 29th, 2015
2015 Nanonics Image Contest January 29th, 2015
Iranian Scientists Use MOFs to Eliminate Dye Pollutants January 29th, 2015
Physics
New pathway to valleytronics January 27th, 2015
Visualizing interacting electrons in a molecule: Scientists at Aalto University and the University of Zurich have succeeded in directly imaging how electrons interact within a single molecule January 26th, 2015
Nanobeaker offers insight into the condensation of atoms January 21st, 2015
Atoms can be in 2 places at the same time: Researchers of the University of Bonn have shown that cesium atoms do not follow welldefined paths January 20th, 2015
Possible Futures
GS7 Graphene Sensor maybe Solution in Fight Against Cancer January 25th, 2015
Nanotechnology in Energy Applications Market Research Report 20142018: Radiant Insights, Inc January 15th, 2015
'Mind the gap' between atomically thin materials December 23rd, 2014
A novel method for identifying the body’s ‘noisiest’ networks November 19th, 2014
Discoveries
Creating new materials with quantum effects for electronics January 29th, 2015
Los Alamos Develops New Technique for Growing HighEfficiency Perovskite Solar Cells: Researchers’ crystalproduction insights resolve manufacturing difficulty January 29th, 2015
Iranian Scientists Use MOFs to Eliminate Dye Pollutants January 29th, 2015
MadeinSingapore rapid test kit detects dengue antibodies from saliva: IBN's MedTech innovation simplifies diagnosis of infectious diseases January 29th, 2015
Announcements
Advantest to Exhibit at SEMICON Korea in Seoul, South Korea February 46 Showcasing Broad Portfolio of Semiconductor Products, Technologies and Solutions January 29th, 2015
Park Systems Announces Innovations in Bio Cell Analysis with the Launch of Park NXBio, the only 3in1 Imaging Nanoscale Tool Available for Life Science Researchers January 29th, 2015
2015 Nanonics Image Contest January 29th, 2015
Iranian Scientists Use MOFs to Eliminate Dye Pollutants January 29th, 2015
Interviews/Book Reviews/Essays/Reports/Podcasts/Journals/White papers
Discovery Channel taps Angstron Materials for segment featuring graphene advances January 29th, 2015
Asteroid Mining 101: A New Book by WorldRenowned Expert Dr. John S. Lewis  Exclusive SneakPeek Opportunity for Book Reviewers and Media January 29th, 2015
Los Alamos Develops New Technique for Growing HighEfficiency Perovskite Solar Cells: Researchers’ crystalproduction insights resolve manufacturing difficulty January 29th, 2015
Iranian Scientists Use MOFs to Eliminate Dye Pollutants January 29th, 2015
Printing/Lithography/Inkjet/Inks
Toyocolor to Launch New Carbon Nanotube Materials at nano tech 2015 January 24th, 2015
Teijin to Participate in Nano Tech 2015 January 22nd, 2015
A new step towards using graphene in electronic applications January 14th, 2015
Nanoshaping method points to future manufacturing technology December 11th, 2014
Quantum nanoscience
Creating new materials with quantum effects for electronics January 29th, 2015
Nanoscale Mirrored Cavities Amplify, Connect Quantum Memories: Advance could lead to quantum computing and the secure transfer of information over longdistance fiber optic networks January 28th, 2015
New pathway to valleytronics January 27th, 2015
Graphene brings quantum effects to electronic circuits January 22nd, 2015