KMS quantum symmetric states

Abstract

Let $A$ be a unital C${}^{\ast }$-algebra and let $\sigma$ be a one-parameter automorphism group of $A$. We consider ${\mathrm{QSS}}_{\sigma }(A)$, the set of all quantum symmetric states on ${\ast }_1^{\infty }A$ that are also KMS states (for a fixed inverse temperature, for specificity taken to be $-1$) for the free product automorphism group ${\ast }_1^{\infty }\sigma$. We characterize the elements of ${\mathrm{QSS}}_{\sigma }(A)$, we show that ${\mathrm{QSS}}_{\sigma }(A)$ is a Choquet simplex whenever it is nonempty and we characterize its extreme points.

14 pages

References in corpus (2)

• Quantum Symmetry Groups of Finite Spaces
• A noncommutative de Finetti theorem: Invariance under quantum permutations is equivalent to freeness with amalgamation