Research Interests: Quantum information theory, operator theory, linear algebra, and matrix analysis, with current focus on private quantum channels (quantum cryptography), positive operator valued measures (POVMs), quantum fidelity (probability of state transfer), majorization and trumping, and measures of quantum coherence.
My research is funded through a Canada Research Chair (2017-2022), a Canada Foundation for Innovation (CFI) John R. Evans Leaders Fund (JELF) (2017), and a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant (2014-2019).
Prospective Highly Qualified Personnel (HQP): At this time, Brandon University does not offer graduate studies in mathematics or a related discipline. However, my adjunct status at the University of Regina, the University of Manitoba, and the University of Guelph allows me to co-supervise M.Sc. and Ph.D. students as well as postdocs at any of the three institutions. I am actively involved with research at these institutions under the broad umbrella of matrix analysis and operator theory with applications to quantum information theory. If you are interested and have some background in these topics, please contact me for more information. If you are an undergraduate student looking for research opportunities, you may wish to consider an NSERC USRA, which allows you to gain experience in research in mathematics over the summer (see me for more details).
Matlab files: As part of the 2017 PIMS Graduate Math Modelling in Industry Workshop (GMMIW), my team of students (Muhammad Zubair, Charlene Chu, Mounada Gbadamassi, Ruwan Chamara Karunanayaka, Naghmeh Shahverdi, and Xiaohong Zhang) created a Matlab program that plots the probability of state transfer over some specified interval of time, specifically looking at unweighted trees with integer spectrum (from “Small integral trees” by A. E. Brouwer). This could be edited for other purposes (e.g. weighted trees). These files are available here (unfortunately I am not able to upload them as .m files or even .txt files due to internal security policy).
Current Highly Qualified Personnel:
- Julius Adili Masanika, M.Sc. student, University of Regina (co-supervision with Doug Farenick), Winter 2019 – present
- Darian McLaren, Undergrad Research Assistant, Summer 2019
- Farrah Huntinghawk, NSERC USRA, Summer 2019
- Xiaohong Zhang, Ph.D. student, University of Manitoba (co-supervision with Steve Kirkland), Fall 2014 – present
Completed Highly Qualified Personnel:
- Darian McLaren, “Quantum random walks”, NSERC Undergraduate Student Research Award (USRA), Summer 2018; “Quantum probability measures”, Honours Topics student; “Quantum state transfer: a linear algebraic approach”, NSERC USRA, Summer 2017
- Shirin Moein, visiting PhD student from Isfahan University of Technology, Isfahan, Iran (with Rajesh Pereira), University of Guelph, Fall 2017 – Spring 2018
- Chris Ramsey, Postdoctoral Fellow, Brandon University, Fall 2017 – Spring 2018
- Farrah Huntinghawk, “Fun math events at the Indigenous People’s Centre”, series of 10 events on campus funded by the Brandon University Students’ Union Work Study Program, Fall 2016 – Winter 2017
- Rebecca Storey, “On the probability of quantum state transfer”, NSERC USRA, Summer 2016
- Bailey Kacsmar, “Topics in Cryptography”, Honours Topics student, Fall 2015
- Ryan Bergen, “Quantum probability measures”, NSERC USRA, Summer 2015
- Whitney Gordon, “The geometric measure of entanglement”, NSERC USRA, Summer 2015
- Amie Teetaert, “Some applications of doubly stochastic matrices”, Honours Topics student, Fall 2014
- Jin Li, “Quantum fidelity”, Honours Topics student, Fall 2014
- Jarrad Perron, “Connections between geometric measures and orders of entanglement”, Brandon University Research Committee (BURC) grant, Summer 2014
(An asterisk is used to identify students who are co-authors and were under my supervision.)
Refereed Conference Proceedings:
 B. Kacsmar*, S. Plosker, and R. Henry, Computing Low-Weight Discrete Logarithms, the 24th Annual Conference on Selected Areas in Cryptography (SAC 2017). In International Conference on Selected Areas in Cryptography, pp. 106-126. Springer, Cham. eprint