Contact Information
Research Areas
Research Interests
- Tensor theory of operator spaces
- Tensor theory of operator systems
- Local structure of operator spaces and operator systems
- Quantum games
- Quantum error correction
- Quantum information theory
Research Description
My research interests are in operator space theory and quantum information theory. In particular, I am interested in the local structure of operator spaces and operator systems, quantum games, and quantum error correction. Recently I have been interested in quantum field theory, and holography. Graduate students are welcome to email me if you are interested in any of these topics.
Courses Taught
- Fall '23:
- Math 490: Quantum Information Theory I: Quantum Channels and Error Correction (30 students)
- Spring '23:
- Math 595: Operator Space Theory (10 students)
- Course Description. Updates and course information will be on our Canvas page. Email me for code.
- Course Outline
- Math 492: Quantum Channels and Error Correction II (5 students)
- Math 415: Applied Linear Algebra (65 students)
- Math 595: Operator Space Theory (10 students)
- Fall '22:
- Math 492: Quantum Channels and Error Correction (8 students)
- Math 415: Applied Linear Algebra (280 students)
- Spring '22:
- Math 492: Select Topics in Quantum Information Theory (16 students)
- Math 415: Applied Linear Algebra (280 students)
- Fall '21:
- Math 125: Elementary Linear Algebra (80 students)
Additional Campus Affiliations
- Seminar Committee Member, Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign
- Affiliate, Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign
- Scholarship Board Member, Sloan University Center of Exemplar Mentoring at Illinois, University of Illinois at Urbana-Champaign
News:
- Felix Leditzky and I organize our ``Quantum Working Group Seminar.'' Fall 2023 we will meet in Lincoln Hall 1066 at 5:00pm.
- Felix Leditzky and I are organizing an introductory sequence of courses in quantum information theory, to be offered in the Department of Mathematics beginning Fall 2023. Part I: ``Quantum Information Theory I: Quantum Channels and Error Correction'' will be taught by me in the Fall 2023 term
Research Visits:
- Department of Mathematics, Texas Christian University, November 2023
- Department of Mathematics, University of Oslo, September 2023
- Department of Mathematics, Purdue University, July 2023
- Department of Physics, Purdue University, April 2023
- Department of Computer Science, Columbia University, December 2022
- Mathematisches Institut, WWU Münster, June-July 2022
- Department of Mathematics, University of Virginia, April 2022
Research Visitors:
- Thomas Sinclair, Purdue University, August 2023
- David Kribs, University of Guelph, April 2023
- Graeme Smith, University of Colorado Boulder, April 2023
- Nima Lashkari, Purdue University, March 2023
- Alexander Müller-Hermes, University of Oslo, November 2022
Upcoming Lectures:
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Colloquium, Texas Christian University, November 2023: Title: TBD
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Lecture, East Coast Operator Algebras Symposium, Purdue University, October 2023, Title: Resource Dependent Complexity of Quantum Channels
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Lecture, Mathematics for Quantum Computation and Many-Body Theory Seminar, University of Oslo, September 2023, Title: Resource Dependent Complexity of Quantum Channels
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Lecture, Recent Developments in Operator Algebras and Quantum Information Theory, AMS Fall Eastern Sectional, University at Buffalo (SUNY), Buffalo, NY, September 2023, Title: Resource Dependent Complexity of Quantum Channels
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Lecture, Analytical and Combinatorial Methods in Quantum Information Theory II, International Centre for Mathematical Sciences, Edinburgh, Scotland, July 2023, Title: An Index for Inclusions of Operator Systems
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Lecture, Workshop III in Von Neumann Algebras and Geometric Group Theory, University of Iowa, April 2023, Title: An Index for Inclusions of Operator Systems
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Lecture, High Energy Theory Physics Seminar, Purdue University, April 2023: Title: An Index for Inclusions of Operator Systems
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Lecture, Operator Algebras Seminar, Purdue University, April 2023, Title: Operator Systems Generated by Projections
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Lecture, Quantum Information and Computing Seminar, University of Delaware, November 2022, Title: An Index for Inclusions of Operator Systems
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Research Scholars Seminar, Discovery Partners Institute, Chicago, IL, September 2022, Title: Quantum Information Theory: an intro from the theoretical viewpoint
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Lecture Series, KnOttawa Summer School, Kansas State University, July 2022, Topic: Quantum Information Theory
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Lecture I: The Postulates of Quantum Mechanics Part I
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Lecture II: The Postulates of Quantum Mechanics Part II
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Lecture III: Quantum Operations and Quantum Noise Part I
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Lecture IV: Quantum Operations and Quantum Noise Part II
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Lecture V: Quantum Error Correction
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Lecture, Kleines Seminar, WWU Münster, June 2022, Title: The Postulates of Quantum Mechanics and Further Observations
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Lecture, Oberseminar C*-algebren, WWU Münster, June 2022, Title: A Universal Representation for Quantum Commuting Correlations
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Lecture, Operator Theory Seminar, University of Virginia, April 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations
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Plenary Lecture, Southeastern Analysis Meeting, University of Florida, March 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations
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Functional Analysis Seminar, University of California San Diego, February 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations
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Department of Mathematics & Statistics Colloquium, San José State University, September 2021, Title: From Correlation Sets to Tensor Products of C*-algebras: The Connes-Kirchberg Problem
Current Undergraduate Students:
- Jihong Cai (Mathematics)
- Abraham Holtermann (Physics)
- Tushar Mohan (Physics)
Past Undergraduate Students:
- Yushan Chen
- Chieh Hsu
- Zeyuan Yu
Recent Publications
- Resource Dependent Complexity of Quantum Channels (with Yidong Chen, Marius Junge, and Peixue Wu) (2023) arXiv:2303.11304 (Accepted Lecture: Beyond IID II, University of Tübingen, Germany, 2023)
- Operator systems generated by projections (with Travis Russell) (2023) arXiv:2302.12951
- An index for inclusions of operator systems (with Colton Griffin and Thomas Sinclair) (2022). arXiv:2203.05710. To appear: Journal of Operator Theory
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Approximating projections by quantum operations (with Colton Griffin, Aneesh Khilnani, and Thomas Sinclair) (2022) arXiv:2203.02627. Published: Linear Algebra and Its Applications. Volume 663 pgs. 178-199
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Matricial Archimedean order unit spaces and quantum correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2109.11671. To appear: Indiana University Mathematics Journal
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A universal representation for quantum commuting correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2102.05827. Published: Annales Henri Poincar\'{e}. Volume 23 (2022), 4489-4520. DOI: 10.1007/s00023-022-01197-7
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An abstract characterization for projections in operator systems (with Travis Russell). (2020) arXiv:2006.03094. Published: Journal of Operator Theory. Volume 90 (2023), 41-72
- R we living in the matrix? (with Rolando de Santiago). Notices of the American Mathematical Society. Volume 66, Number 8, (2019), Pgs. 1216-1224.