Optical Knots Encode Information

Examples of the structure of optical framed knots. (Source: U. Ottawa)

In a world first, researchers from the University of Ottawa in colla­boration with Israeli scientists have been able to create optical framed knots in the laboratory that could poten­tially be applied in modern techno­logies. Their work opens the door to new methods of distributing secret crypto­graphic keys – used to encrypt and decrypt data, ensure secure communi­cation and protect private information. “This is funda­mentally important, in particular from a topo­logy-focused perspec­tive, since framed knots provide a platform for topo­logical quantum computations,” explained Ebrahim Karimi, Canada Research Chair in Structured Light at the Univer­sity of Ottawa. “In addition, we used these non-trivial optical structures as information carriers and developed a security protocol for classical communication where information is encoded within these framed knots.”­

The researchers suggest a simple do-it-yourself lesson to help us better understand framed knots, those three-dimen­sional objects that can also be described as a surface. “Take a narrow strip of a paper and try to make a knot,” said Hugo Larocque, uOttawa alumnus and current PhD student at MIT. “The resulting object is referred to as a framed knot and has very interesting and important mathe­matical features.” The group tried to achieve the same result but within an optical beam, which presents a higher level of diffi­culty. After a few tries (and knots that looked more like knotted strings), the group came up with what they were looking for: a knotted ribbon structure that is quint­essential to framed knots.

“In order to add this ribbon, our group relied on beam-shaping techniques mani­pulating the vectorial nature of light,” explained Hugo Larocque. “By modifying the oscillation direction of the light field along an unframed optical knot, we were able to assign a frame to the latter by gluing together the lines traced out by these oscillating fields.” According to the researchers, structured light beams are being widely exploited for encoding and distributing information. “So far, these applications have been limited to physical quantities which can be recognized by observing the beam at a given position,” said postdoc Dr. Alessio D’Errico. “Our work shows that the number of twists in the ribbon orientation in con­junction with prime number factori­zation can be used to extract a “braid repre­sentation” of the knot.”

“The structural features of these objects can be used to specify quantum infor­mation processing programs,” added Hugo Larocque. “In a situation where this program would want to be kept secret while dissemi­nating it between various parties, one would need a means of encrypting this braid and later deciphering it. Our work addresses this issue by proposing to use our optical framed knot as an encryption object for these programs which can later be recovered by the braid extrac­tion method that we also introduced. For the first time, these complicated 3D structures have been exploited to develop new methods for the distri­bution of secret crypto­graphic keys. Moreover, there is a wide and strong interest in exploiting topo­logical concepts in quantum computation, communication and dissi­pation-free electronics. Knots are described by specific topo­logical properties too, which were not considered so far for crypto­graphic protocols.”

The idea behind the project emerged in 2018, during a discussion with Israeli researchers at a scientific meeting in Crete, Greece. Scientists from Ben-Gurion University of the Negev and Bar-Ilan University, in Israel, developed the prime number encoding protocol. The project then crossed the Medi­terranean Sea and the Atlantic Ocean before ending up in Karimi’s lab located in the Advanced Research Complex at the Univer­sity of Ottawa. That’s where the experimental procedure was developed and conducted. The resulting data were then analyzed, and the braid structure extracted through a specially devised program.

“Current techno­logies give us the possi­bility to manipulate, with high accuracy, the different features charac­terizing a light beam, such as intensity, phase, wavelength and polari­zation,” said Hugo Larocque. “This allows to encode and decode infor­mation with all-optical methods. Quantum and classical crypto­graphic protocols have been devised exploiting these different degrees of freedom. Our work opens the way to the use of more complex topo­logical structures hidden in the propagation of a laser beam for distri­buting secret crypto­graphic keys.” “Moreover, the experimental and theo­retical techniques we developed may help find new experimental approaches to topological quantum compu­tation, which promises to surpass noise-related issues in current quantum computing techno­logies,” added Ebrahim Karimi. (Source: U. Ottawa)

Reference: H. Larocque et al.: Optical framed knots as information carriers, Nat. Commun. 11, 5119 (2020); DOI: 10.1038/s41467-020-18792-z

Link: Structural Quantum Optics (E. Karimi), Dept. of Physics, University of Ottawa, Ottawa, Canada

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