2023/06/02 by James Fullwood, Fullwood, James, Arthur J. Parzygnat +1 · 4 citations
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2306.01831
openalex publication_date 2023/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we use the theory of quantum states over time to define an entropy S(ρ,E) associated with quantum processes (ρ,E), where ρ is a state and E is a quantum channel responsible for the dynamical evolution of ρ. The entropy S(ρ,E) is a generalization of the von Neumann entropy in the sense that S(ρ,id)=S(ρ) (where id denotes the identity channel), and is a dynamical analogue of the quantum joint entropy for bipartite states. Such an entropy is then used to define dynamical formulations of the quantum conditional entropy and quantum mutual information, and we show such information measures satisfy many desirable properties, such as a quantum entropic Bayes' rule. We also use our entropy function to quantify the information loss/gain associated with the dynamical evolution of quantum systems, which enables us to formulate a precise notion of information conservation for quantum processes.