## Nathan Johnston

Assistant professor

### Contact Information

- njohnston@mta.ca
- Phone
- (506) 364-2633
- Office
- DUNN 224
- Office hours
- Mon. 12:30 p.m. - 1:30 p.m. and Wed. 1:30 p.m. - 2:30 p.m.
- Other websites

### Research interests

My main research interests lie with solving mathematical and
computational problems motivated by questions in quantum information
theory. In particular, I make use of linear algebra, matrix
analysis, and convex optimization to tackle questions related to the theory of quantum
entanglement. My recent work has focused on investigating how things like matrix norms and eigenvalues can reveal properties of quantum entanglement, and finding methods to determine whether a given
quantum state is separable or entangled.

### Teaching

Mount Allison University

Winter 2016

MATH 3221 (Advanced Linear Algebra)

Fall 2015

MATH 2111 (Multivariable Calculus)

MATH 2221 (Linear Algebra)

University of Waterloo

Summer 2014

QIC 890/891 (Module 2: Entanglement Detection) - course notes (PDF)

University of Guelph

Fall 2011

MATH 2200 (Advanced Calculus I)

Fall 2010

MATH 2000 (Set Theory)

### Education

University of Guelph, Guelph, ON

Bachelor of Arts (2007)

M.Sc. Mathematics (2008)

Ph.D. Mathematics (2012)

### Publications

Peer-Reviewed Journal Articles

- N. Johnston and D. W. Kribs. Duality of entanglement norms.
*Houston Journal of Mathematics*, 41(3):831–847, 2015. - 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. - S. Arunachalam, N. Johnston, and V. Russo. Is absolute separability determined by the partial transpose?
*Quantum Information & Computation*, 15(7 & 8):0694–0720, 2015. - 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. - N. Johnston. The structure of qubit unextendible product bases.
*Journal of Physics A: Mathematical and Theoretical*, 47:424034, 2014. - G. Gutoski and N. Johnston. Process tomography for unitary quantum channels.
*Journal of Mathematical Physics*, 55:032201, 2014. - N. Johnston. Separability from spectrum for qubit–qudit states.
*Physical Review A*, 88:062330, 2013. - 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. - N. Johnston. Non-positive partial transpose subspaces can be as large as any entangled subspace.
*Physical Review A*, 87:064302, 2013. - N. Johnston. Non-uniqueness of minimal superpermutations.
*Discrete Mathematics*, 313:1553–1557, 2013. - N. Johnston, Ł. Skowronek, and E. Størmer. Generation of mapping cones from small sets.
*Linear Algebra and Its Applications*, 438:3062–3075, 2013. - N. Johnston and E. Størmer. Mapping cones are operator systems.
*Bulletin of the London Mathematical Society*, 2012. doi: 10.1112/blms/bds006 - N. Johnston and D. W. Kribs. Quantum gate fidelity in terms of Choi matrices.
*Journal of Physics A: Mathematical and Theoretical*, 44:495303, 2011. - N. Johnston. Characterizing operations preserving separability measures via linear preserver problems.
*Linear and Multilinear Algebra*, 59(10):1171–1187, 2011. - 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. - 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. - N. Johnston and D. W. Kribs. Generalized multiplicative domains and quantum error correction.
*Proceedings of the American Mathematical Society*, 139:627–639, 2011. - N. Johnston and D. W. Kribs. A family of norms with applications in quantum information theory.
*Journal of Mathematical Physics*, 51:082202, 2010. - 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. - 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

- 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 - 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 - 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 - 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. - 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

- 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.

Theses

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

Unpublished Papers

- M. Piani, M. Cianciaruso, T. R. Bromley, C. Napoli, N. Johnston, and G. Adesso. Robustness of asymmetry and coherence of quantum states. E-print: arXiv:1601.03782 [quant-ph], 2016.
- 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. E-print: arXiv:1601.03781 [quant-ph], 2016.
- N. Johnston, R. Mittal, V. Russo, and J. Watrous. Extended nonlocal games and monogamy-of-entanglement games. E-print: arXiv:1510.02083 [quant-ph], 2015.
- N. Johnston.
*The complexity of the puzzles of Final Fantasy XIII-2*. E-print: arXiv:1203.1633 [cs.CC], 2012. - N. Johnston.
*Partially entanglement breaking maps and right CP-invariant cones*. Unpublished notes, 2008.