Donuts, math, and superdense teleportation of quantum information

Siv Schwink
5/28/2015

Professor Paul Kwiat
Professor Paul Kwiat
Physics Illinois doctoral candidate Trent Graham
Physics Illinois doctoral candidate Trent Graham

 

 

 

 

 

 

 

 

 

 

 

Putting a hole in the center of the donut—a mid-nineteenth-century invention—allows the deep-fried pastry to cook evenly, inside and out. As it turns out, the hole in the center of the donut also holds answers for a type of more efficient and reliable quantum information teleportation, a critical goal for quantum information science.

Quantum teleportation is a method of communicating information from one location to another without moving the physical matter to which the information is attached. Instead, the sender (Alice) and the receiver (Bob) share a pair of entangled elementary particles—in this experiment, photons, the smallest units of light—that transmit information through their shared quantum state. In simplified terms, Alice encodes information in the form of the quantum state of her photon. She then sends a key to Bob over traditional communication channels, indicating what operation he must perform on his photon to prepare the same quantum state, thus teleporting the information.

Quantum teleportation has been achieved by a number of research teams around the globe since it was first theorized in 1993, but current experimental methods require extensive resources and/or only work successfully a fraction of the time.

In superdense teleportation of quantum information, Alice (near) selects a particular set of states to send to Bob (far), using the hyperentangled pair of photons they share. The possible states Alice may send are represented as the points on a donut shape, here artistically depicted in sharp relief from the cloudy silhouette of general quantum state that surrounds them. To transmit a state, Alice makes a measurement on her half of the entangled state, which has four possible outcomes shown by red, green, blue, and yellow points.  She then communicates the outcome of her measurement (in this case, yellow, represented by the orange streak connecting the two donuts) to Bob using a classical information channel. Bob then can make a corrective rotation on his state to recover the state that Alice sent. Image by Precision Graphics, copyright Paul Kwiat, University of Illinois at Urbana-Champaign
In superdense teleportation of quantum information, Alice (near) selects a particular set of states to send to Bob (far), using the hyperentangled pair of photons they share. The possible states Alice may send are represented as the points on a donut shape, here artistically depicted in sharp relief from the cloudy silhouette of general quantum state that surrounds them. To transmit a state, Alice makes a measurement on her half of the entangled state, which has four possible outcomes shown by red, green, blue, and yellow points. She then communicates the outcome of her measurement (in this case, yellow, represented by the orange streak connecting the two donuts) to Bob using a classical information channel. Bob then can make a corrective rotation on his state to recover the state that Alice sent. Image by Precision Graphics, copyright Paul Kwiat, University of Illinois at Urbana-Champaign
Now, by taking advantage of the mathematical properties intrinsic to the shape of a donut—or torus, in mathematical terminology—a research team led by physicist Paul Kwiat of the University of Illinois at Urbana-Champaign has made great strides by realizing “superdense teleportation”. This new protocol, developed by coauthor physicist Herbert Bernstein of Hampshire College in Amherst, MA, effectively reduces the resources and effort required to teleport quantum information, while at the same time improving the reliability of the information transfer.

With this new protocol, the researchers have experimentally achieved 88 percent transmission fidelity, twice the classical upper limit of 44 percent. The protocol uses pairs of photons that are “hyperentangled”—simultaneously entangled in more than one state variable, in this case in polarization and in orbital angular momentum—with a restricted number of possible states in each variable. In this way, each photon can carry more information than in earlier quantum teleportation experiments.

At the same time, this method makes Alice’s measurements and Bob’s transformations far more efficient than their corresponding operations in quantum teleportation: the number of possible operations being sent to Bob as the key has been reduced, hence the term “superdense”.

Kwiat explains, “In classical computing, a unit of information, called a bit, can have only one of two possible values—it’s either a zero or a one. A quantum bit, or qubit, can simultaneously hold many values, arbitrary superpositions of 0 and 1 at the same time, which makes faster, more powerful computing systems possible.

“So a qubit could be represented as a point on a sphere, and to specify what state it is, one would need longitude and latitude. That’s a lot of information compared to just a 0 or a 1.”

“What makes our new scheme work is a restrictive set of states. The analog would be, instead of using a sphere, we are going to use a torus, or donut shape. A sphere can only rotate on an axis, and there is no way to get an opposite point for every point on a sphere by rotating it—because the axis points, the north and the south, don’t move. With a donut, if you rotate it 180 degrees, every point becomes its opposite. Instead of axis points you have a donut hole. Another advantage, the donut shape actually has more surface area than the sphere, mathematically speaking—this means it has more distinct points that can be used as encoded information.”

Lead author, Illinois physics doctoral candidate Trent Graham, comments, “We are constrained to sending a certain class of quantum states called ‘equimodular’ states. We can deterministically perform operations on this constrained set of states, which are impossible to perfectly perform with completely general quantum states. Deterministic describes a definite outcome, as opposed to one that is probabilistic. With existing technologies, previous photonic quantum teleportation schemes either cannot work every time or require extensive experimental resources. Our new scheme could work every time with simple measurements.”

This research team is part of a broader collaboration that is working toward realizing quantum communication from a space platform, such as the International Space Station, to an optical telescope on Earth. The collaboration—Kwiat, Graham, Bernstein, physicist Jungsang Kim of Duke University in Durham, NC, and scientist Hamid Javadi of NASA’s Jet Propulsion Laboratory in Pasadena, CA—recently received funding from NASA Headquarter's Space Communication and Navigation program (with project directors Badri Younes and Barry Geldzahler) to explore the possibility.

“It would be a stepping stone toward building a quantum communications network, a system of nodes on Earth and in space that would enable communication from any node to any other node,” Kwiat explains. “For this, we’re experimenting with different quantum state properties that would be less susceptible to air turbulence disruptions.”

The team’s recent experimental findings are published in the May 28, 2015 issue of Nature Communications, and represent the collaborative effort Kwiat, Graham, and Bernstein, as well as physicist Tzu-Chieh Wei of State University of New York at Stony Brook, mathematician Marius Junge of the University of Illinois.

 

This research is funded by NSF Grant No. PHY-0903865, NASA NIAC Program, and NASA Grant No. NNX13AP35A.  It is partially supported by National Science Foundation Grants DMS-1201886, No. PHY 1314748, and No. PHY 1333903.

Recent News

  • Partnerships

The Chicago Quantum Exchange, a growing intellectual hub for the research and development of quantum technology, has expanded its community to include new industry partners working at the forefront of quantum technology and research. These corporate partners are Boeing, Applied Materials, Inc., ColdQuanta, Inc., HRL Laboratories LLC and Quantum Opus LLC.

Together, the Chicago Quantum Exchange and its new industry partners will focus on developing a new understanding of the rules of quantum mechanics, leading to breakthroughs in quantum devices, materials and computing techniques.

Based at the University of Chicago’s Pritzker School of Molecular Engineering, the Chicago Quantum Exchange is anchored by the University of Chicago, the U.S. Department of Energy’s Argonne National Laboratory and Fermi National Accelerator Laboratory (both operated for DOE by the University of Chicago), and the University of Illinois at Urbana-Champaign, and includes the University of Wisconsin-Madison and Northwestern University.

  • In the Media
  • Alumni News

Oscar Rodrigo Araiza Bravo, a 2014 MHS graduate, recently was granted a full scholarship to Harvard University to earn a PhD in physics. He graduated with a straight A average from the University of Illinois-Urbana/Champaign with degrees in mathematics and engineering physics.

After completing doctoral studies he hopes to become a college professor who does both teaching and research. “I enjoy teaching. If you ever want to find out whether or not you know a subject, teach it,” Araiza Bravo said.

  • In the Media

There have been accusations for years that the Major League ball is “juiced,” thus accounting for the increasing power numbers.

MLB officials have categorically denied that, and last year, commissioned a study of the baseball and how it’s produced.

In the landmark 85-page independent report replete with color graphs, algorithms and hypotheses, a group of 10 highly-rated professors and scientists chaired by Alan Nathan determined that the ball is not livelier or “juiced.” Nathan is a professor emeritus of physics from the University of Illinois at Urbana Champaign.

The surge in home runs “seems, instead, to have arisen from a decrease in the ball’s drag properties, which cause it to carry further than previously, given the same set of initial conditions – exit velocity, launch and spray angle, and spin. So, there is indirect evidence that the ball has changed, but we don’t yet know how,” wrote Leonard Mlodinow, in the report’s eight-page executive summary.