Roy Araiza

Profile picture for Roy Araiza

Contact Information

257A Altgeld Hall (MC-382), Department of Mathematics, University of Illinois at Urbana- Champaign, 1409 West Green Street, Urbana, Illnois, 61801 USA
raraiza@illinois.edu

Research Areas

Analysis
Physical Mathematics
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J.L. Doob Research Assistant Professor
Affiliate, Illinois Quantum Information Science and Technology Center
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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 field theory

Research Description

My research interests are in operator space theory and quantum theory. In particular, I am interested in the local structure of operator spaces and operator systems, quantum games, quantum error correction, quantum field theory and holography. Graduate students are welcome to email me if you are interested in any of these topics. 

Courses Taught

  1. Spring '24: 
    1. Math 432: Set Theory and Topology (32 students)
    2. Math 492: Winter Spaces and the Stabilizer Formalism (6 students)
  2. Fall '23: 
    1. Math 490: Quantum Information Theory I: Quantum Channels and Error Correction (30 students)
      1. Course Description
  3. Spring '23:
    1. Math 595: Operator Space Theory (10 students)
      1. Course Description. Updates and course information will be on our Canvas page. Email me for code.
      2. Course Outline
    2. Math 492: Quantum Channels and Error Correction II (5 students)
    3. Math 415: Applied Linear Algebra (65 students)
  4. Fall '22:
    1. Math 492: Quantum Channels and Error Correction (8 students)
    2. Math 415: Applied Linear Algebra (280 students)
  5. Spring '22:
    1. Math 492: Select Topics in Quantum Information Theory (16 students)
    2. Math 415: Applied Linear Algebra (280 students)
  6. Fall '21: 
    1. Math 125: Elementary Linear Algebra (80 students)

Additional Campus Affiliations

  1. Seminar Committee Member, Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign
  2. Affiliate, Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign
  3. 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.'' We meet on Mondays at 5:00pm. Spring 2024 location: Lincoln 1022
  • 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: 

  1. Department of Mathematics, Texas Christian University, November 2023
  2. Department of Mathematics, University of Oslo, September 2023
  3. Department of Mathematics, Purdue University, July 2023
  4. Department of Physics, Purdue University, April 2023
  5. Department of Computer Science, Columbia University, December 2022
  6. Mathematisches Institut, WWU Münster, June-July 2022
  7. Department of Mathematics, University of Virginia, April 2022

Research Visitors:

  1. Carlos Palazuelos,Universidad Complutense Madrid, March 2024
  2. Thomas Sinclair, Purdue University, August 2023
  3. David Kribs, University of Guelph, April 2023
  4. Graeme Smith, University of Colorado Boulder, April 2023
  5. Nima Lashkari, Purdue University, March 2023
  6. Alexander Müller-Hermes, University of Oslo, November 2022

Upcoming Lectures: 

  1. Lecture, Operator Algebras, Quantum Information, and Computation, AMS Fall Central Sectional, University of Texas San Antonio, San Antonio, TX, September 2024, Title: TBD

  2. Lecture, Sandia National Laboratories, Albuquerque, New Mexico, April 2024, Title: TBD

  3. Lecture, Operator System Day, University of Delaware, February 2024, Title: A Stabilizer Formalism via Winter Spaces

  4. Colloquium, Department of Mathematics, Purdue University, November 2023, Title: An Axiomatic Approach to Quantum Complexity Measures

  5. Frank Jones Memorial Colloquium, Texas Christian University, November 2023, Title: An Axiomatic Approach to Quantum Complexity Measures

  6. Lecture, East Coast Operator Algebras Symposium, Purdue University, October 2023, Title: Resource Dependent Complexity of Quantum Channels

  7. Lecture, Mathematics for Quantum Computation and Mody-Body Theory Seminar, September 2023, Title: Resource Dependent Complexity of Quantum Channels

  8. 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

  9. 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

  10. Lecture, Workshop III in Von Neumann Algebras and Geometric Group Theory, University of Iowa, April 2023, Title: An Index for Inclusions of Operator Systems

  11. Lecture, High Energy Theory Physics Seminar, Purdue University, April 2023: Title: An Index for Inclusions of Operator Systems

  12. Lecture, Operator Algebras Seminar, Purdue University, April 2023, Title: Operator Systems Generated by Projections

  13. Lecture, Quantum Information and Computing Seminar, University of Delaware, November 2022, Title: An Index for Inclusions of Operator Systems

  14. Research Scholars Seminar, Discovery Partners Institute, Chicago, IL, September 2022, Title: Quantum Information Theory: an intro from the theoretical viewpoint

  15. Lecture Series, KnOttawa Summer School, Kansas State University, July 2022, Topic: Quantum Information Theory 

    1. Lecture I: The Postulates of Quantum Mechanics Part I

    2. Lecture II: The Postulates of Quantum Mechanics Part II

    3. Lecture III: Quantum Operations and Quantum Noise Part I

    4. Lecture IV: Quantum Operations and Quantum Noise Part II

    5. Lecture V: Quantum Error Correction

  16. Lecture, Kleines Seminar, WWU Münster, June 2022, Title: The Postulates of Quantum Mechanics and Further Observations

  17. Lecture, Oberseminar C*-algebren, WWU Münster, June 2022, Title: A Universal Representation for Quantum Commuting Correlations

  18. Lecture, Operator Theory Seminar, University of Virginia, April 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations

  19. Plenary Lecture, Southeastern Analysis Meeting, University of Florida, March 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations

  20. Functional Analysis Seminar, University of California San Diego, February 2022, Title: Matricial Archimedean Order Unit Spaces and Quantum Correlations

  21. 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: 

  1. Jihong Cai (Mathematics)
  2. Tushar Mohan (Physics): SULI Inter, Brookhaven National Lab, May-August 2024

Past Undergraduate Students: 

  1. Abraham Holtermann (Physics)
  2. Yushan Chen
  3. Chieh Hsu, First position: Masters at École Normale Supérieure -PSL
  4. Zeyuan Yu

 

Recent Publications

  1. Nonsignalling values of quantum games and the tripartite Grothendieck inequality (with Marius Junge and Carlos Palazuelos) In preparation.
  2. Asymptotic tensor powers of operator spaces (with Alexander Müller-Hermes) In preparation.
  3. A note on the stabilizer formalism via noncommutative graphs (with Jihong Cai, Yushan Chen, Abraham Holtermann, Chieh Hsu, Tushar Mohan, Peixue Wu and Zeyuan Yu) (2023) arXiv: 2310.00762. Published: Quantum Information Processing. DOI: 10.1007/s11128-024-04291-3 (2024)
  4. Resource dependent complexity of quantum channels (with Yidong Chen, Marius Junge, and Peixue Wu) (2023) arXiv:2302.11304v2
  5. Lipschitz complexity (with Yidong Chen, Marius Junge, and Peixue Wu) (2023) arXiv:2303.11304v3 (Accepted Lecture: Beyond IID II, University of Tübingen, Germany, 2023)
  6. Operator systems generated by projections (with Travis Russell) (2023) arXiv:2302.12951 
  7. An index for inclusions of operator systems (with Colton Griffin and Thomas Sinclair) (2022). arXiv:2203.05710. To appear: Journal of Operator Theory

  8. 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

  9. Matricial Archimedean order unit spaces and quantum correlations (with Travis Russell and Mark Tomforde). (2021) arXiv:2109.11671. To appear: Indiana University Mathematics Journal

  10. 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

  11. 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

  12. R we living in the matrix? (with Rolando de Santiago). Notices of the American Mathematical Society. Volume 66, Number 8, (2019), Pgs. 1216-1224.