2025/06/04 by Roy Araiza, Marius Junge, Araiza, Roy +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2506.04197
openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a noncommutative optimal transport framework for quantum channels acting on von Neumann algebras. Our central object is the Lipschitz cost measure, a transportation-inspired quantity that evaluates the minimal cost required to move between quantum states via a given channel. Accompanying this is the Lipschitz contraction coefficient, which captures how much the channel contracts the Wasserstein-type distance between states. We establish foundational properties of these quantities, including continuity, dual formulations, and behavior under composition and tensorization. Applications include recovery of several mathematical quantities including expected group word length and Carnot-Carathéodory distance, via transportation cost. Moreover, we show that if the Lipschitz contraction coefficient is strictly less than one, one can get entropy contraction and mixing time estimates for certain classes of non-symmetric channels.