Welcome to Vern Paulsen's home page
Professor Vern Paulsen
Operator Algebra Methods in QIT, QIC 890-002/PMATH 950-002
11:30--12:50 T Th, QNC 1201
Course Notes: Notes v6
Homework Assignments: Homework 1 ,
Homework 2 , Homework 3 ,
Measure and Integration, Pmath 451/651,
12:30--1:20, MWF, QNC 1508
Final Exam, Friday, December 13, 2019, 9--11 AM, MC 4060
A Survey of Functional Analysis Methods for QIT, QIC 890-003,
11:30--1 MW, QNC 1201
FAQI Chapter 1
\\ FAQI Chapter 2(updated)
\\ FAQI Chapter 3
Completely Bounded Maps, PMath 950, Section 6383
Time and Room: 10--11:30 M W, MC5479
A survey of Functional Analysis Methods for QIT, PMath 990, QIC 890,
10--11:30 T Th, QNC 1201
Measure and Integration, PMath 451,
2:30--4 T Th, RCH 109
Final Exam: Saturday, April 21, 2018, 4--6:30pm, PAC Upper 11
Winter 2017, PMath 810--Banach algebras and operator theory, T-Th, 9:30--11:00
Fall 2016, A Survey of Functional Analysis Methods for QIT, PMath 990, or QIC 890, M-W, 10--11:30, QNC 1201
Winter 2016, Entanglement and Non-Locality, PMath 990, Tu-Th 12:00-1:20, QIC 890
Fall 2015, PMath 990, Matrix Analysis, MWF 2:30-3:20, M3-2134
Homework Assignments Updated: 11/27
Course Notes Updated: 11/19
Research interests: Operator Algebras, Operator Theory, Frame Theory, Reproducing Kernel Hilbert Spaces, Quantum Computation and Quantum Information Theory.
Curriculum Vita, including a list of all publications
Former PhD students:
Copies of some of my student's theses are available here.
An Introduction to the Theory of Reproducing Kernel Hilbert Spaces, Cambridge Studies in Advanced Mathematics, 152, Cambridge University Press, 2016.
This is a collection of errata for the RKHS book:Errata
Completely Bounded Maps and Operator Algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, 2003.
Solutions to Selected Exercises Prepared by Mrinal Ragupathi Solutions Manual .
Matrix range characterizations of operator system properties
(with Benjamin Passer)
Bisynchronous Games and Factorizable Maps(with Mizanur
Rahaman) arXiv Link
Bigalois extensions and the graph isomorphism game (with
Michael Brannan, Alexandru Chirvasitu, Kari Eifler, Samuel Harris,
Xiaoyu Su, Mateusz Wasilewski), Communications in Mathematical
10.1007/s00220-019-03563-9 arXiv link , CMP link
Constant gap between conventional strategies and those based on
C*-dynamics for self-embezzlement(with Richard Cleve, Benoit
Collins, Li Liu)
Schur multipliers and mixed unitary maps(with Samuel J. Harris,
Rupert H. Levene, Sarah Plosker, and Mizanur Rahaman) Journal of
Mathematical Physics 59, 112201 (2018);
https://doi.org/10.1063/1.5066242 arXiv link
Preservation of the joint essential matricial range(with
C.-K. Li and Y.-T. Poon) Bull. Lond. Math. Soc. 51 (2019), no. 5, 868–876;
Entanglement breaking rank(with S. Pandey, J. Prakash, and
M. Rahaman) arXiv link
Perfect strategies for non-signalling games(with M. Lupini,
L. Mancinska, D. E. Roberson, G. Scarpa, S. Severini, I. G. Todorov, A.
Winter) February 2020, Mathematical Physics Analysis and Geometry 23(1)
Eventually Entanglement Breaking Maps(with S. Jaques and
M. Rahaman), J. Math. Phys. 59 (2018), no. 6, 062201, 11 pp.
Composition of PPT maps(with M. Kennedy and N. Manor), Quantum
Information and Computation, Vol. 18, No. 5&6 (2018) 0472–0480 arXiv link
Complexity and capacity bounds for quantum channels(with R. Levene and
I. Todorov), IEEE Transactions on Information Theory, Vol. 64, No. 10, October 2018, 6917–6928. arXiv link
Non-closure of the set of quantum correlations via graphs(with
K. Dykema and J. Prakash), Comm. Math. Phys. 365 (2019), no. 3,
The Delta Game(with K. Dykema and J. Prakash), Quantum Inf. Comput. 18 (2018), no. 7-8, 599–616. arXiv link
A synchronous game for binary constraint systems(with S.-J. Kim
and C. Schafhauser), Journal of Mathematical Physics 59, 032201 (2018); doi:
Reverse Cholesky factorization and tensor products of nest
algebras(with H.J. Woerdeman),
Proc. Amer. Math. Soc. 146 (2018), no. 4, 1693–1698. arXiv link
Algebras, synchronous games and chromatic numbers of
graphs(with J.W. Helton, K.P. Meyer, and M. Satriano), New York J. Math. 25 (2019), 328–361. Expanded Version
Complete spectral sets and numerical range(with K.R. Davidson
and H.J. Woerdeman), Proc. Amer. Math. Soc. 146 (2018), no. 3, 1189–1195. arXiv link
Unitary correlation sets(with S.J. Harris), Integral Equations Operator Theory 89 (2017), no. 1, 125–149. arXiv link
Perfect Embezzlement of Entanglement(with R. Cleve and L. Liu)
J. Math. Phys., 58, 012204
Tensor Products of the Operator System Generated by the Cuntz Isometries(with D. Zheng), J. Operator Theory 76:1(2016), 67-91 doi: 10.7900/jot.2015aug04.2093 arXiv link
Quantum Graph Homomorphisms via Operator Systems(with C. Ortiz) ArXiv Abstract Linear Alg. and Appl., Vol 497, 15 May 2016, 23-43, doi: 10.1016/j.laa2016.02.019
The SOH Operator System(with W. Ng) J. Operator Theory 76 (2016), no. 2, 285–305. ArXiv Abstract
Correlation Minimizing Frames in Small Dimensions(with G. Getzelman and N. Leonhard)Arxiv Abstract
Synchronous Correlation Matrices and Connes' Embedding Conjecture(with K. Dykema), Journal of Mathematical Physics, 57, 015215 http://dx.doi.org/10.1063/1.4936751 Arxiv Abstract
Extensions of the Inequalities of Hardy and Hilbert(with D. Singh)Arxiv Abstract
The Functional Analysis of Quantum Information Theory(edited by Ved Prakash Gupta, Prabha Mandayam, V. S. Sunder)Arxiv Abstract
A Spectral Characterization of AN Operators(with S. Pandey),
Journal of the Australian Mathematical Society, 102(2017), no.3, 369-391 Journal Link
Lovasz theta type norms and Operator Systems(with C. Ortiz) Arxiv Abstract Linear Alg. and Appl., Vol. 477, 15 July 2015, 128-147, doi: 10.1016/j.laa.2015.03.022
Estimating Quantum Chromatic Numbers(with S. Severini, D. Stahlke, I. Todorov and A. Winter)arXiv link J. Funct. Anal. 270 (2016), no. 6, 2188?2222.
Quantum chromatic numbers via operator systems(with I. Todorov) Arxiv Abstract Q. J. Math. 66(2015), no. 2, 677-692.
Characterisations of the weak expectation property(with D. Farenick, A.S. Kavruk, and I. Todorov)Arxiv Abstracts New York Journal of Mathematics, Volume 24a (2018), 107-135.
Complete positivity of the map from a basis to its dual basis(with F. Shultz) Arxiv Abstract Journal of Mathematical Physics 54 072201 (2013); http://dx.doi.org/10.1063/1.4812329
The isomorphism relation for separable C*-algebras(with G.A. Elliott, I. Farah, C. Rosendal, A.S. Toms, and A. Tornquist) Arxiv Abstract Math. Res. Lett. 20(2013), no. 6, 1071-1080.
Operator Systems from Discrete Groups(with D. Farenick, A.S. Kavruk and I. Todorov) Arxiv Abstract, Communications in Mathematical Physics, April 2014, DOI 10.1007/s00220-014-2037-6
C*-algebras with the weak expectation property and a multivariable analogue of Ando's theorem on the numerical radius(with D. Farenick and A. Kavruk) Arxiv Abstract, J. Operator Theory 70 (2013), no. 2, 573?590.
Operator system quotients of matrix algebras and their tensor products(with D. Farenick) Arxiv Abstract Mathematica Scandinavica, Vol. 111, 2012, 210-243.
An approximation theorem for nuclear operator systems(with K.H. Han) Arxiv Abstract J. Funct. Anal., Vol. 261, 2011, 999-1009.
Minimal and Maximal Operator Spaces and Operator Systems in Entanglement Theory(with D. Kribs, N. Johnston and R. Pereira) JKPP_Aug31.pdf , J. Funct. Anal., Vol. 260, Issue 8, 2011, 2407-2423.
Quotients, exactness and nuclearity in the operator system category(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract Advances in Math., Vol. 235, 1 March 2013, 321-360.
The Feichtinger conjecture and reproducing kernel Hilbert spaces(with S. Lata) Arxiv Abstract, Indiana Univ. Math. J. 60 (2011), no. 4, 1303?1317.
Spanning and independence properties of frame partitions(with B. Bodmann, P. Casazza and D. Speegle) Arxiv Abstract, Proceedings of the AMS, Volume 140, Number 7, July 2012, 2193-2207.
Syndetic Sets and Amenability Arxiv Abstract, Proceedings of the AMS, Volume 140, Number 6, June 2012, 1997-2001.
Syndetic Sets, Paving and the Feichtinger Conjecture Arxiv Abstract, Proceedings of the AMS, Vol. 139, No. 3, March 2011, 1115-1120.
Tensor Products of Operator Systems(with A. Kavruk, I. Todorov and M. Tomforde) Arxiv Abstract, J. Funct. Anal, 261(2011), 267-299.
Operator algebras of functions(with M. Mittal) Arxiv Abstract, J. Funct. Anal., 258(2010), 3195-3225.
Operator System Structures on Ordered Spaces(with I. Todorov and M. Tomforde) Arxiv Abstract, Proc. of the LMS, 102(1)(2011), 25-49.
Stable Isomorphism of Dual Operator Spaces(with G. Eleftherakis and I. Todorov) Arxiv Abstract, J. Funct. Anal., 258(2010), 260-278.
Weak expectations and the injective envelope Arxiv Abstract, TAMS, Volume 363, Number 9, September 2011, 4735-4755.
An operator algebraic proof of Agler's factorization theorem(with S. Lata and M. Mittal)Arxiv Abstract PAMS, Vol. 137, No. 11, Nov. 2009, 3741-3748.
A Constrained Nevanlinna-Pick Interpolation Problem(with K.R. Davidson, M. Raghupathi, and D. Singh)
Arxiv Abstract IUMJ, Vol. 58, No. 2, 2009, 709--732.
Representations of logmodular algebras(with M. Raghupathi) Arxiv Abstract TAMS, Vol. 363, No. 5, May 2011, 267-240.
Equiangular Tight Frames from Complex Seidel Matrices Containing Cube Roots of Unity (with B. Bodmann and M. Tomforde) Arxiv Abstract LAA, 430(2009), 396--417.
Computing stabilized norms for quantum operations via the theory of completely bounded maps(with N. Johnston and D. Kribs) Arxiv Abstract , Quantum Inf. Comput., 9(2009), no. 1-2, 16-35.
Vector Spaces with an Order Unit(with M. Tomforde) Arxiv Abstract , IUMJ, 58(2009), no. 3, 1319-1359.
Injectivity and projectivity in analysis and topology(with D. Hadwin) Arxiv Abstract Sci. China Math. 54 (2011), no. 11, 2347?2359.
Lectures on the Kadison-Singer Problem Lecture Notes
A dynamical systems approach to the Kadison-Singer problemArxiv Abstract, J. Funct. Anal., 255(2008), 120--132.
Some new equivalences of Anderson's paving conjectures(with M. Ragupathi)Arxiv Abstract, Proc. AMS, Vol. 136, No. 12, Dec. 2008, 4275-4282.
Stably Isomorphic Dual Operator Algebras(with G.K. Eleftherakis) Arxiv Abstract, Math. Ann., (2008)341:99--112.
Projections and the Kadison-Singer Problem(with P. Casazza, D. Edidin and D. Kalra) Abstract Matrices and Operators, to appear.
State extensions and the Kadison-Singer Problem(with C. Akemann) ARCC-ap.pdf, AIM preprint.
Injective and projective Hilbert C*-modules, and C*-algebras of compact operators(with M. Frank) Abstract
Interpolation and balls in C^k(with J. Solazzo) Abstract JOT, 60:2(2008), 379--398.
Decoherence-insensitive quantum communication by optimal C*-encoding(with B. Bodmann and D. Kribs), Abstract IEEE Transactions on Information Theory, Vol. 53, Number 12, December 2007, 4738--4749.
Smooth frame-path termination for Higher Order Sigma-Delta Quantization(with S. Abdulbaki and B. Bodmann) HOSD-JFAA.pdf JFAA, Vol. 13, Issue 3(2007), 285--307.
Frame Paths and Error Bounds for Sigma-Delta Quantization(with B. Bodmann) sigmadelta.pdf Appl. Comput. Harmon. Anal. 22(2007), no. 2, 176-197.
Equivariant Maps and Bimodule Projections solelprob.pdf JFA 240(2006), 495-507.
Loss-Insensitive Vector Encoding with Two-Uniform Frames(with B. Bodmann) FGE_SPIE.pdf, in Wavelets XI, Proceedings of the SPIE, vol. 5914(2005), M. Papadakis, A.F. Laine, M.A. Unser (Eds.), pp. 591403-1-12.
A Simple Proof of Bohr's Inequality(with D. Singh) bohrconf.pdf
An Introduction to the Theory of Topological Groups and Their Representations, Course Notes grouprepn.pdf
Modules Over Subalgebras of the Disk Algebra(with D. Singh) diskalg.pdf IUMJ, Vol. 55, No. 5(2006), 1751-1766.
Schur multipliers and operator-valued Foguel-Hankel operators(with C. Badea), Abstract,, IUMJ, Vol. 50, No. 4(2001), 1509--1522.
Frames, Graphs and Erasures(with B. Bodmann), Abstract, LAA 404(2005), 118-146.
Extensions of Bohr's Inequality(with D. Singh) bohrext.dvi file Bull. LMS 38(2006), 991-999.
Two Reformulations of Kadison's Similarity Problem(with D. Hadwin) kadsim.dvi file JOT, Vol. 55, No. 1, Winter 2006, 3-16.
Quasimultipliers of Operator Spaces(with M. Kaneda), quasi.dvi file JFA, 217(2004), 347-365. Reprints available.
Injective Envelopes of C*-algebras as Operator Modules (with M. Frank), Pac.J. Math., 212(2003), 57-69.
Characterizations of Essential Ideals as Operator Modules (with M. Kaneda), J.O.T., 49(2003), 245-262.
Diffusing with Stefan and Maxwell (with N.R. Amundson and T.-W. Pan), AIChE, April 2003, Vol.49, No. 4, 813-830.
Optimal Frames for Erasures (with R.B. Holmes), Lin. Alg. Appl., 377(2004), 31-51.
Reprints available. opframe.pdf
Bohr's Inequality for Uniform Algebras (with D. Singh) PAMS, 132(2004), 3577-3579. Reprints available.
Lie ideals in Operator Algebras(with A. Hopenwasser), J.O.T.,52(2004), 325-340, reprints available, posted on arXiv
On the Ranges of Bimodule Projections(with A. Katavolos), Can. Bull. Math., 48(1), 2005, 97-111, reprints available, Arxiv Abstract
Embezzlement of Entanglement, BIRS, July 25, 2019, Video
Slofstra's Contributions to the Connes Embeddding Problem
BIRS, July 15, 2019,
Preservation of the Joint Essential Matrical Range CMS,
Regina, June 9, 2019, Slides
Constant Gap for Self-Embezzlement CMS, Regina, June 8, 2019,
Quantum probabilities, synchronous games and C*-algebras,
Shanks Workshop, Vanderbilt University, September 15, 2018, Slides
Reverse Cholesky Factorisation CMS, December 9, 2017
Perfect Embezzlement, Connes and Tsirelson COSY, Thunder Bay,
May 2017, Slides
C*-algebras and synchronous games Institut Henri Poincare,
September 12, 2017 YouTube
Numerical Ranges and Spectral Sets CMS, December 3, 2016 Slides
Quantum Chromatic Numbers GPOTS, UIUC, May 26, 2016, Slides
Operator Systems: Quotients, Duals and Tensors with Applications to Connes' Embedding Problem Banff International Research Station, February 27, 2012 Video
The Functional Analysis of Quantum Information Theory, I, Chennai, India, January 2, 2011, Youtube
The Functional Analysis of Quantum Information Theory, II, Chennai, India, January 3, 2011, Youtube
The Functional Analysis of Quantum Information Theory, III, Chennai, India, January 4, 2011, Youtube
The Functional Analysis of Quantum Information Theory, IV, Chennai, India, January 5, 2011, Youtube
The Functional Analysis of Quantum Information Theory, V, Chennai, India, January 6, 2011, Youtube
Applications of Injective Envelopes AMS, Baltimore, 2003, Slides
Last updated: November 15, 2019