'Classified knots': Researchers create optical framed knots to encode information

Date:
October 16, 2020
Source:
University of Ottawa
Summary:
Researchers 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.



FULL STORY ==========================================================================
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. The group recently published their findings in Nature Communications.


========================================================================== "This is fundamentally important, in particular from a topology-focused perspective, since framed knots provide a platform for topological quantum computations," explained senior author, Professor 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 concept
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 first
author 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 uOttawa Postdoctoral Fellow and co-author of this study, 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
so-called "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 origins 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 Dr. 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.

The applications "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 Dr. Ebrahim Karimi.


========================================================================== Story Source: Materials provided by University_of_Ottawa. Note: Content
may be edited for style and length.


========================================================================== Journal Reference:
1. Hugo Larocque, Alessio D'Errico, Manuel F. Ferrer-Garcia, Avishy
Carmi,
Eliahu Cohen, Ebrahim Karimi. Optical framed knots as
information carriers. Nature Communications, 2020; 11 (1) DOI:
10.1038/s41467-020- 18792-z ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2020/10/201016181039.htm

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