Robustness of Fixed Points of Quantum Channels and Application to Approximate Quantum Markov Chains

Watch a 26-minute conference talk from the 19th Theory of Quantum Computation, Communication and Cryptography Conference (TQC 2024) exploring the robustness of fixed points in quantum channels and their applications to approximate quantum Markov chains. Discover how to find new quantum channels and states that satisfy exact fixed point equations when given a quantum channel and state that is almost a fixed point. Learn about the affirmative solutions developed through compactness arguments under general assumptions, and examine explicit bounds on approximation errors for various examples including general quantum states, unitary channels, and unital channels. Explore the dimensional scaling challenges in bipartite quantum systems with locally acting channels, and understand the application of these findings to quantum Markov chains, particularly in establishing dimension-dependent upper bounds for tripartite quantum states as their conditional mutual information approaches zero. Presented by researchers Robert Salzmann, Bjarne Bergh, and Nilanjana Datta at OIST, Japan, this theoretical quantum information science presentation advances understanding of quantum channel properties and their practical implications.