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

  • In the Media

Paul Kwiat asks his volunteers to sit inside a small, dark room. As their eyes adjust to the lack of light, each volunteer props his or her head on a chin rest—as you would at an optometrist’s—and gazes with one eye at a dim red cross. On either side of the cross is an optical fiber, positioned to pipe a single photon of light at either the left or the right side of a volunteer’s eye.

Even as he verifies the human eye’s ability to detect single photons, Kwiat, an experimental quantum physicist at the University of Illinois at Urbana–Champaign, and his colleagues are setting their sights higher: to use human vision to probe the very foundations of quantum mechanics, according to a paper they submitted to the preprint server arXiv on June 21.

  • Research
  • Biological Physics

Scientists at the University of Illinois at Urbana-Champaign have predicted new physics governing compression of water under a high-gradient electric field. Physics Professor Aleksei Aksimentiev and his post doctoral researcher James Wilson found that a high electric field applied to a tiny hole in a graphene membrane would compress the water molecules travelling through the pore by 3 percent. The predicted water compression may eventually prove useful in high-precision filtering of biomolecules for biomedical research.

  • Research
  • Biological Physics
  • Biophysics

A new synthetic enzyme, crafted from DNA rather than protein, flips lipid molecules within the cell membrane, triggering a signal pathway that could be harnessed to induce cell death in cancer cells.   

Researchers at University of Illinois at Urbana-Champaign and the University of Cambridge say their lipid-scrambling DNA enzyme is the first in its class to outperform naturally occurring enzymes – and does so by three orders of magnitude. They published their findings in the journal Nature Communications.

  • Accolades
  • High Energy Physics

Assistant Professor of Physics Thomas Faulkner has been selected by the US Department of Energy (DOE) Office of Science to receive an Early Career Award. The DOE Early Career Research Program, now in its ninth year, provides award recipients with significant funding over a five year period. Faulkner is among 84 scientists at U.S. universities and DOE-supported national laboratories to be selected this year. He is one of only two scientists at the University of Illinois at Urbana-Champaign to receive the honor this year.

The Early Career Award recognizes promising scientists within 10 years of having earned their doctoral degrees, working in research areas supported by the DOE Office of Science. Faulkner’s research proposal in theoretical high-energy physics is entitled, “New perspectives on QFT and gravity from quantum entanglement.”