Publications

This page contains information about all of my publications, both published and pending. Note that some entries below contain links to additional discussion, code, or slides that are not included with the publications themselves.

Books

  1. N. Johnston and D. Greene. Conway’s Game of Life: Mathematics and Construction. Self-published, 2022. doi: 10.5281/zenodo.6097284
  2. N. Johnston. Advanced Linear and Matrix Algebra. Springer International Publishing, 2021.
  3. N. Johnston. Introduction to Linear and Matrix Algebra. Springer International Publishing, 2021.

Peer-Reviewed Journal Articles

  1. N. Johnston and S. Plosker. Laplacian {-1,0,1}- and {-1,1}-diagonalizable graphs. Linear Algebra and its Applications, 704:309–339, 2025.
  2. R. Houston, A. P. Goucher, and N. Johnston. A new formula for the determinant and bounds on its tensor and Waring ranks. Combinatorics, Probability and Computing, 33(6):769–794, 2024.
  3. J. Holbrook, N. Johnston, and J.-P. Schoch. Real Schur norms and Hadamard matrices. Linear and Multilinear Algebra, 72:1967–1984, 2024.
  4. N. Johnston and L. Pipes. Bounding Real Tensor Optimizations via the Numerical Range. Electronic Journal of Linear Algebra, 39:289–306, 2023.
  5. N. Johnston, B. Lovitz, and A. Vijayaraghavan. Complete hierarchy of linear systems for certifying quantum entanglement of subspaces. Physical Review A, 106:062443, 2022.
  6. N. Johnston, S. Moein, R. Pereira, and S. Plosker. Birkhoff-James orthogonality in the trace norm, with applications to quantum resource theories. Electronic Journal of Linear Algebra, 38:760–776, 2022.
  7. N. Johnston, S. Moein, R. Pereira, and S. Plosker. Absolutely k-Incoherent Quantum States and Spectral Inequalities for Factor Width of a Matrix. Physical Review A, 106:052417, 2022.
  8. N. Johnston and J. Sikora. Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes). Linear Algebra and its Applications, 653:395–429, 2022.
  9. B. Lovitz and N. Johnston. Entangled subspaces and generic local state discrimination with pre-shared entanglement. Quantum, 6:760, 2022.
  10. G. Champagne, N. Johnston, M. MacDonald, and L. Pipes. Spectral properties of symmetric quantum states and symmetric entanglement witnesses. Linear Algebra and its Applications, 649:273–300, 2022.
  11. N. Johnston, B. Lovitz, and D. Puzzuoli. The non-m-positive dimension of a positive linear map. Quantum 3:172, 2019.
  12. N. Johnston and O. MacLean. Pairwise completely positive matrices and conjugate local diagonal unitary invariant quantum states. Electronic Journal of Linear Algebra, 35:156–180, 2019.
  13. 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.
  14. 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.
  15. N. Johnston and E. Patterson. The inverse eigenvalue problem for entanglement witnesses. Linear Algebra and Its Applications, 550:1–27, 2018.
  16. N. Johnston, S. Kirkland, S. Plosker, R. Storey, and X. Zhang. Perfect quantum state transfer using Hadamard-diagonalizable graphs. Linear Algebra and its Applications, 531:375–398, 2017.
  17. 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.
  18. N. Johnston, R. Mittal, V. Russo, and J. Watrous. Extended nonlocal games and monogamy-of-entanglement games. Proceedings of the Royal Society A, 472, 2016. DOI: 10.1098/rspa.2016.0003
  19. C. Napoli, T. R. Bromley, M. Cianciaruso, M. Piani, N. Johnston, and G. Adesso. Robustness of coherence: An operational and observable measure of quantum coherence, Physical Review Letters, 116:150502, 2016.
  20. M. Piani, M. Cianciaruso, T. R. Bromley, C. Napoli, N. Johnston, and G. Adesso. Robustness of asymmetry and coherence of quantum states, Physical Review A, 93:042107, 2016.
  21. N. Johnston and D. W. Kribs. Duality of entanglement norms. Houston Journal of Mathematics, 41(3):831–847, 2015.
  22. S. Bandyopadhyay, A. Cosentino, N. Johnston, V. Russo, J. Watrous, and N. Yu. Limitations on separable measurements by convex optimization. IEEE Transactions on Information Theory, 61(6):3593–3604, 2015.
  23. S. Arunachalam, N. Johnston, and V. Russo. Is absolute separability determined by the partial transpose? Quantum Information & Computation, 15(7 & 8):0694–0720, 2015.
  24. J. Chen and N. Johnston. The minimum size of unextendible product bases in the bipartite case (and some multipartite cases). Communications in Mathematical Physics, 333(1):351-365, 2015.
  25. N. Johnston. The structure of qubit unextendible product bases. Journal of Physics A: Mathematical and Theoretical, 47:424034, 2014.
  26. G. Gutoski and N. Johnston. Process tomography for unitary quantum channels. Journal of Mathematical Physics, 55:032201, 2014.
  27. N. Johnston. Separability from spectrum for qubit–qudit states. Physical Review A, 88:062330, 2013.
  28. J. Chen, H. Dawkins, Z. Ji, N. Johnston, D. W. Kribs, F. Shultz, and B. Zeng. Uniqueness of quantum states compatible with given measurement results. Physical Review A, 88:012109, 2013.
  29. N. Johnston. Non-positive partial transpose subspaces can be as large as any entangled subspace. Physical Review A,  87:064302, 2013.
  30. N. Johnston. Non-uniqueness of minimal superpermutations. Discrete Mathematics, 313:1553–1557, 2013.
  31. N. Johnston, Ł. Skowronek, and E. Størmer. Generation of mapping cones from small sets. Linear Algebra and Its Applications, 438:3062–3075, 2013.
  32. N. Johnston and E. Størmer. Mapping cones are operator systems. Bulletin of the London Mathematical Society, 2012. doi: 10.1112/blms/bds006
  33. N. Johnston and D. W. Kribs. Quantum gate fidelity in terms of Choi matrices. Journal of Physics A: Mathematical and Theoretical, 44:495303, 2011.
  34. N. Johnston. Characterizing operations preserving separability measures via linear preserver problems. Linear and Multilinear Algebra, 59(10):1171–1187, 2011.
  35. N. Johnston, D. W. Kribs, V. I. Paulsen, and R. Pereira. Minimal and maximal operator spaces and operator systems in entanglement theory. Journal of Functional Analysis, 260(8):2407–2423, 2011.
  36. N. Johnston and D. W. Kribs. A family of norms with applications in quantum information theory II. Quantum Information & Computation, 11(1 & 2):104–123, 2011.
  37. N. Johnston and D. W. Kribs. Generalized multiplicative domains and quantum error correction. Proceedings of the American Mathematical Society, 139:627–639, 2011.
  38. N. Johnston and D. W. Kribs. A family of norms with applications in quantum information theory. Journal of Mathematical Physics, 51:082202, 2010.
  39. M.-D. Choi, N. Johnston, and D. W. Kribs. The multiplicative domain in quantum error correction. Journal of Physics A: Mathematical and Theoretical, 42:245303, 2009.
  40. N. Johnston, D. W. Kribs, and V. Paulsen. Computing stabilized norms for quantum operations. Quantum Information & Computation, 9(1 & 2):16–35, 2009.

Refereed Conference Proceedings

  1. N. Johnston, B. Lovitz, and A. Vijayaraghavan. Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond. In Proceedings of the 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS), 2023. doi:10.1109/FOCS57990.2023.00079
  2. N. Johnston. The minimum size of qubit unextendible product bases. In Proceedings of the 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC), 2013. doi: 10.4230/LIPIcs.TQC.2013.93
  3. N. Johnston. Norm duality and the cross norm criteria for quantum entanglement. Linear and Multilinear Algebra (Proceedings of the 12th Workshop on Numerical Ranges and Numerical Radii), 2013. doi: 10.1080/03081087.2012.753595
  4. N. Johnston and D. W. Kribs. A family of norms with applications in entanglement theory. In Proceedings of the 2011 ICO International Conference on Information Photonics (IP), 2011. doi: 10.1109/ICO-IP.2011.5953727
  5. N. Johnston and D. W. Kribs. Schmidt operator norms and entanglement theory. In Proceedings of the Fourth International Conference on Quantum, Nano and Micro Technologies, 92–95, 2010.
  6. N. Johnston, D. W. Kribs, and C.-W. Teng. An operator algebraic formulation of the stabilizer formalism for quantum error correction. Acta Applicandae, 108(3):687–696, 2009.

Book Chapters

  1. N. Johnston. Some Beautiful and Difficult Questions about Cellular Automata. In Designing Beauty: The Art of Cellular Automata, A. Adamatzky and G. J. Martinez (eds.), Springer International Publishing, pages 59–63, 2016.
  2. N. Johnston. The B36/S125 “2×2” Life-like cellular automaton. In Game of Life Cellular Automata chapter 7, A. Adamatzky, Springer-UK, 99–114, 2010.

Book Reviews

  1. N. Johnston. Review: The Mathematics of Cellular Automata. By Jane Hawkins, American Mathematical Society, 2024. The American Mathematical Monthly, 1–6, 2024. doi:10.1080/00029890.2024.2417565

Course Notes

  1. Advanced Linear and Matrix Algebra [zip file containing PDFs] – notes for a 12-week advanced linear algebra course (MATH 3221 at Mount Allison University)
  2. Introduction to Linear and Matrix Algebra [zip file containing PDFs] – notes for a 12-week introductory linear algebra course (MATH 2221 at Mount Allison University)
  3. Entanglement Detection [pdf] – notes for the four-lecture module on entanglement detection taught as part of QIC 890/891 at the University of Waterloo in Spring 2014

Theses

  1. N. Johnston. Norms and Cones in the Theory of Quantum Entanglement. PhD thesis, University of Guelph, 2012.
  2. N. Johnston. Stabilized Distance Measures and Quantum Error Correction. Master’s thesis, University of Guelph, 2008.

Unpublished Papers

  1. H. Derksen, N. Johnston, B. Lovitz, and A. Vijayaraghavan. X-arability of mixed quantum states. E-print: arXiv:2409.18948 [quant-ph], 2024.
  2. N. Johnston, S. Moein, and S. Plosker. The factor width rank of a matrix. E-print: arXiv:2405.11556 [math.CO], 2024.
  3. N. Johnston, V. Russo, and J. Sikora. Tight bounds for antidistinguishability and circulant sets of pure quantum states. E-print: arXiv:2311.17047 [quant-ph], 2023.
  4. N. Johnston, B. Lovitz, and A. Vijayaraghavan. A hierarchy of eigencomputations for polynomial optimization on the sphere. E-print: arXiv:2310.17827 [math.OC], 2023.
  5. N. Johnston. The complexity of the puzzles of Final Fantasy XIII-2. E-print: arXiv:1203.1633 [cs.CC], 2012.
  6. N. Johnston. Partially entanglement breaking maps and right CP-invariant cones. Unpublished notes, 2008.