# Research

**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 Graduate Students:**

Xiaohong Zhang, Ph.D. student, University of Manitoba (co-supervisor with Steve Kirkland), Fall 2014 – present

Shirin Moein, visiting Ph.D. student from Isfahan University of Technology, Isfahan, Iran (with Rajesh Pereira), hosted at the University of Guelph, Fall 2017 – Spring 2018

**Recent Undergraduate Student Research Supervision:**

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;

Rebecca Storey, “On the probability of quantum state transfer”, NSERC Undergraduate Student Research Award (USRA), Summer 2016

Bailey Kacsmar, “Topics in Cryptography”, Honours Topics student, Fall 2015

Ryan Bergen, “Quantum probability measures”, NSERC Undergraduate Student Research Award (USRA), Summer 2015

Whitney Gordon, “The geometric measure of entanglement”, NSERC Undergraduate Student Research Award (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

**Publications:**

(An asterisk is used to identify students who are co-authors and were under my supervision.)

[19] S. Plosker and C. Ramsey*. *An operator-valued Lyapunov theorem*, Journal of Mathematical Analysis and Applications, accepted. arxiv

[18] S. Kirkland, D. Mclaren*, R. Pereira, S. Plosker, and X. Zhang*. *Perfect quantum state transfer in weighted paths with potentials (loops) using orthogonal polynomials*, Linear and Multilinear Algebra, accepted. arxiv

[17] N. Johnston, C.-K. Li, and S. Plosker. *The modified trace distance of coherence is constant on most pure states*, Journal of Physics A: Mathematical and Theoretical, **51**, 414010, 2018. arxiv

[16] N. Johnston, C.-K. Li, S. Plosker, Y.T. Poon, and B. Regula. *Evaluating the robustness of k-coherence and k-entanglement**, Physical Review A, ***98**, 022328, 2018. arxiv

[15] N. Johnston, S. Kirkland, S. Plosker, R. Storey*, and X. Zhang*. *Perfect quantum state transfer using Hadamard diagonalizable weighted graphs*. Linear Algebra and its Applications, ** 531, **pp. 375-398, 2017. arxiv

[14] J. Chen, S. Grogan, N. Johnston, C.-K. Li, and S. Plosker. *Quantifying the coherence of pure quantum states*. Physical Review A, **94**, 042313, 2016. arxiv

[13] W. Gordon*, S. Kirkland, C.-K, Li, S. Plosker, and X. Zhang*. *Bounds on probability of state transfer with respect to readout time and edge weight*. Physical Review A, **93**, 022309, 2016. arxiv

[12] D. Farenick, M.J. Kozdron, and S. Plosker. *Spectra and variance of quantum random variables*. Journal of Mathematical Analysis and Applications, **434**, pp. 1106-1122, 2016. arxiv

[11] M. E. Carrington, G. Kunstatter, J. Perron*, and S. Plosker. *On the geometric measure of entanglement for pure states*. Journal of Physics A: Mathematical and Theoretical, **48**, 435302, 2015. arxiv

[10] J. Li*, R. Pereira and S. Plosker. *Some geometric interpretations of quantum fidelity*. Linear Algebra and its Applications, **487**, pp. 158-171, 2015. arxiv

[9] R. Pereira and S. Plosker. *Extending a characterization of majorization to infinite dimensions*. Linear Algebra and its Applications, **468**, pp. 80-86, 2015. arxiv

[8] T. Jochym-O’Connor, D. W. Kribs, R. Laflamme, and S. Plosker. *Quantum subsystems: Exploring the complementarity of quantum privacy and error correction. *Physical Review A, **90**, 032305, 2014. arxiv

[7] D. W. Kribs and S. Plosker. *Private quantum codes: introduction and* *connection with higher rank numerical ranges*. Linear and Multilinear Algebra, **62**, pp. 639-647, 2014. arxiv

[6] D. W. Kribs, R. Pereira, and S. Plosker. *Trumping and power majorization*. Linear and Multilinear Algebra, **61**, pp. 1455-1463, 2013. arxiv

[5] T. Jochym-O’Connor, D. W. Kribs, R. Laflamme, and S. Plosker. *Private **quantum subsystems*. Physical Review Letters, **111**, 030502, 2013. arxiv

[4] R. Pereira and S. Plosker. *Dirichlet polynomials, majorization, and trumping*. Journal of Physics A: Mathematical and Theoretical, **46**, 225302, 2013. arxiv

[3] D. Farenick, R. Floricel, and S. Plosker. *Approximately clean quantum probability measures*. Journal of Mathematical Physics, **54**, Issue 5, 052201, 2013.

[2] D. Farenick, S. Plosker, and J. Smith.* Classical and nonclassical randomness in quantum measurements*. Journal of Mathematical Physics, **52**, Issue 12, 122204, 2011. arxiv

[1] A. Church, D. W. Kribs, R. Pereira, and S. Plosker. *Private quantum **channels, conditional expectations, and trace vectors*. Quantum Information & Computation (QIC), **11**, no. 9 & 10, pp. 774 – 783, 2011. arxiv