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Explore the fundamental concepts of quantum reference frames in this comprehensive lecture delivered by Anne-Catherine de la Hamette as part of the Solstice of Foundations 2025 summer school program. Delve into the theoretical foundations that underpin how quantum systems can serve as reference frames for describing other quantum systems, examining the mathematical formalism and physical principles that govern these quantum mechanical constructs. Learn about the role of symmetries in quantum mechanics and how reference frames emerge naturally from the relational nature of quantum descriptions. Discover the implications of treating reference frames themselves as quantum objects rather than classical entities, and understand how this perspective transforms our understanding of fundamental physics concepts such as time, space, and measurement. Examine the connection between quantum reference frames and gauge theories, exploring how different choices of reference frames can lead to equivalent physical descriptions. Investigate the practical applications of quantum reference frames in quantum information processing, quantum communication protocols, and foundational studies of quantum mechanics. This lecture forms part of a comprehensive summer school program on quantum computing organized by the University of Zurich's Institute of Physics and Digital Society Initiative, with support from the Pauli Center for Theoretical Studies and Squids: Schools for Quantum Information Development.
