Let’s say you and your cousin inherit some money and you both have a version of the will on your computer. What is the minimum amount of information your computers need to share to determine if the versions are the same?
This hypothetical scenario poses a communication complexity problem. These problems deal with how much information you need to exchange, from computer to computer or from network node to node, to perform a particular task or function. The less information is transferred to get the job done, the more energy and time is saved – and the more privacy is preserved.
Li Qian and Hoi-Kwong-Lo, both professors in the Edward S. Rogers Sr. Department of Electrical and Computer Engineering at the University of Toronto in the Faculty of Applied Sciences and Engineering, and Xiaoqing Zhong, a PhD student in the Physics Department of the Faculty of Arts, developed an improved Quantum Fingerprinting (QF) protocol to more efficiently and securely solve these type of problems that arise in contexts such as computer networks and Very Large Scale Integration (VLSI) chip design , among other things.
The team’s protocol used the many different frequencies of the quantum state of a photon – a novel approach – to encode information. Your paper was recently published in Nature communication.
“Suppose you and your cousin each have a million bytes – one megabyte of data file,” says Qian. âIn the classic protocol, the smallest ‘fingerprint’ required to determine whether the information is the same – with a certainty of almost 100 percent – is found using the square root of the total number of bits. So a one megabyte file would require approximately 300 bytes to be transferred. With quantum fingerprinting, the amount scales logarithmically: A file with one megabyte would only need about three bytes. “
The benefit becomes even more apparent as the files get larger, adds Qian.
“As the data string gets bigger and bigger, quantum fingerprinting can drastically reduce the amount of information you have to exchange.”
The QF protocol is achieved by taking advantage of a property called superposition. In classical communication, a photon encodes information as either one or zero, but in quantum mechanics a photon can exist in many states between these binary values. The possible combinations of these intermediate states enable each individual photon to carry far more information, reduce the total number and save time, energy and bandwidth.
“It also greatly reduces information leaks,” says Qian, “which reduces privacy and security concerns.”
A challenge in implementing the QF is that the detectors used to register the photons are very sensitive and can generate signal noise. Currently, superconducting photon detectors have to be housed in cryogenic dewars that cool the environment to milli-Kelvin temperatures. Nevertheless, random errors creep in.
The team’s improved QF protocol used a technique called “multiplexing” – the simultaneous sending and measuring of multiple frequencies of photons – to speed communication time and make QF much less susceptible to detector noise. In the laboratory, they demonstrated this measurement with six frequencies, but in principle it could be thousands, says Qian.
âIt makes QF a more practical option,â she says. “We can use standard components: standard semiconductor-based single-photon detectors, which are orders of magnitude cheaper than superconductor detectors.”
Although QF is an accessible technology in today’s marketplace, quantum communication is hindered by a lack of compatible infrastructure. Quantum signals are fragile and, while they can coexist with the classical signal in our current fiber optic network, can easily become contaminated. Many of the data terminals in the existing network, such as amplifiers, switches and routers, are not suitable for quantum signals.
Further research – ongoing in Qian and Lo’s joint laboratories – needs to be done to merge quantum and classical signals into the same fiber.
âIn engineering there is often a balance between the practical and the theoretical,â says Professor Deepa Kundu, Chair of the Department of Electrical Engineering and Information Technology. âAnd the research by Professors Qian and Lo is a great example of this. You have refined a state-of-the-art protocol with a view to the future telecommunications landscape – and are thus contributing to its implementation. “
When asked what motivated her to work on quantum technologies, Qian points out the uniqueness of the quantum properties.
âThey just can’t be found anywhere else in nature,â she says. âImagine how the unique property of lasers – coherent light – has revolutionized optical technologies in just a few decades. I am convinced that the quantum properties of photons will do the same. “