Journal of Operator Theory

Volume 91, Issue 2, Spring 2024 pp. 567-593.

An index for inclusions of operator systems

Authors: Colton Griffin (1), Thomas Sinclair (2)
Author institution: (1) Department of Mathematics and Illinois Quantum Information Science and Technology Center, University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.
(2) Mathematics Department, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, U.S.A.

Summary: Inspired by a well-known characterization of the index of an inclusion of II$_1$ factors due to Pimsner and Popa, we define an index-type invariant for inclusions of operator systems. We compute examples of this invariant, show that it is multiplicative under minimal tensor products, and explain how it generalizes the Lovasz theta invariant to general matricial systems in a manner that is closely related to the quantum Lovasz theta invariant defined by Duan, Severini, and Winter.

DOI: http://dx.doi.org/10.7900/jot.2022jun27.2420
Keywords: operator systems, noncommutative entropy theory, quantum information theory

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