2007/06/19 by Wojciech Roga, M. Fannes, Mark Fannes +2 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Bipartite graph #Combinatorics #Conditional quantum entropy #Entropy (arrow of time) #Generalized relative entropy #Joint quantum entropy #Mathematics #Maximum entropy thermodynamics #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Quantum discord #Quantum entanglement #Quantum mechanics #Quantum mutual information #Quantum relative entropy #Quantum state #Statistical physics #Subadditivity #Von Neumann entropy #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/3/035305
published as J. Phys. A: Math. Theor. 41 (2008) 035305 · 25 pages, no figures
arxiv created 2007/06/19 · openalex publication_date 2008/01/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the composition of quantum maps acting on a simple quantum system. It induces a semi-group in the subset of states with maximally mixed partial traces. Subadditivity of the von Neumann entropy with respect to this product is proved. It is equivalent to subadditivity of the entropy of bistochastic maps with respect to their composition, where the entropy of a map is the entropy of the corresponding state under the Jamiołkowski isomorphism. Strong dynamical subadditivity of a concatenation of three bistochastic maps is established. Analogous bounds for the entropy of a composition are derived for general stochastic maps. In the classical case they lead to new bounds for the entropy of a product of two stochastic matrices.