Improving Quantum Communications

As cyber threats such as eavesdropping continue to rise, leading to stolen data, Quantum communication has become a way to create secure networks and maintain data privacy. Quantum communication allows for the transfer of quantum bits, a bit which can represent 0 and 1 at the same time, which is different than a traditional bit which is either 0 or 1. If a hacker tries to eavesdrop on a quantum bit, the quantum bit will collapse into either a 0 or 1 showing that someone has attacked the system.

One of the most important quantum communication frameworks is the “Local (Quantum) Operations and Classical Communication” (LOCC) protocol, which allows for the use of local quantum operations between direct classical communication. An important concept in quantum communication is the distinguishability of quantum states - a mathematical object to describe the quantum system at a point in time. The ability to tell quantum states apart, also called distinguishability, is used in quantum tasks such as information processing, key distribution and error detection.

Today’s quantum communication research aims to better understand and improve knowledge of which graph characteristics can be used to distinguish between quantum states.

Distinguishability using Chordal Graphs

University of Guelph Department of Mathematics and Statistics professors Drs. David Kribs and Rajesh Pereira collaborated with University of Waterloo researcher Dr. Comfort Mintah (who began the work as a PhD student at Guelph) and Dr. Michael Nathanson of Harvard University to explore a new method for improving the distinguishability between quantum states. Their research establishes the characteristics of chordal graphs (a unique type of graph in graph theory) as the backbone of state distinguishability.

The research has two main contributions: the first demonstrates that one-way distinguishability is linked with chordal graph structures, and the second demonstrates that non-distinguishability is linked to graph structures that are far away from being chordal.

For distinguishability, concepts such as orthogonality, Gram matrices, and Positive Operator-Valued Measures (POVMs) are used in a multi-step series of theorems and corollaries to prove that chordal graphs paired with one-way LOCC aid in identifying distinguishable states.

For the second part, the research focuses on using non-chordal graphs to better understand the characteristics related to indistinguishability. Concepts and characteristics such as a minimum rank parameter and Haemers number are discussed, along with orthogonal graph representation and independent sets.

Both distinguishability and indistinguishability are important concepts in quantum communication, specifically related to privacy in communications.

Advancing Quantum Communications Research

The research findings improve quantum communications security through the exploration of distinguishability and indistinguishability in quantum states. These concepts can be applied to keep data secure from eavesdropping and various other attacks.

“Research findings are expected to be important as quantum technologies continue to develop and need to mesh with existing classical infrastructure. Additionally, LOCC is an important theoretical tool for probing mysterious quantum phenomena such as entanglement,” said Kribs.

This story was written by Izabela Savić as part of the Science Communicators: Research @ CEPS initiative. Izabela is a MSc candidate in the School of Computer Science under Dr. Xiaodong Lin. Her research focus is on network security and computer forensics to better equip law enforcement and user security.

The work on distinguishability in quantum communication is supported by the National Sciences and Engineering Research Council (NSERC) of Canada.

Reference: D. W. Kribs, C. Mintah, M. Nathanson, R. Pereira, “Chordal graphs and distinguishability of quantum product states,” Linear Algebra and its Applications, vol 694, pp. 478-498, 2024. Doi: 10.1016/j.laa.2024.04.021