Coupling capacity in C*-algebras
Journal article, 2023

Given two unital C*-algebras equipped with states and a positive operator in the enveloping von Neumann algebra of their minimal tensor product, we define three parameters that measure the capacity of the operator to align with a coupling of the two given states, and establish a duality formula that shows the equality of two of the parameters. Restricting to abelian C*-algebras we recover instances of Monge-Kantorovich duality and establish a connection with quantitative versions of Arveson's Null Set Theorem. On the other hand, restricting to matrix algebras we recover and generalise quantum versions of Strassen's Theorem. We show that in the latter case our parameters can detect maximal entanglement and separability.

quantum channel

coupling capacity

quantum coupling

C

measures of entanglement

-algebra

Author

Adam Skalski

Polish Academy of Sciences

Ivan G. Todorov

University of Delaware

Lyudmyla Turowska

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

0308-2105 (ISSN) 1473-7124 (eISSN)

Vol. In Press

Roots

Basic sciences

Subject Categories

Mathematical Analysis

DOI

10.1017/prm.2023.81

More information

Latest update

5/14/2024