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Explore topological order in open quantum systems through this conference lecture delivered at the International Centre for Theoretical Sciences. Delve into the fundamental concepts of how topological phases of matter behave when subjected to environmental interactions and decoherence effects. Examine the theoretical framework for understanding how topological properties can be preserved or modified in non-isolated quantum systems, including the role of dissipation and noise in topological quantum states. Learn about the mathematical tools and physical principles used to analyze topological order beyond the traditional closed system paradigm. Investigate specific examples of how topological phases respond to various types of environmental coupling and discover the implications for quantum information processing and topological quantum computing. Gain insights into current research directions in this rapidly evolving field that bridges quantum many-body physics, open quantum systems theory, and topological condensed matter physics. This presentation forms part of a comprehensive program on generalized symmetries and anomalies in quantum phases of matter, providing advanced perspectives on how symmetry principles apply to realistic quantum systems with environmental interactions.
