Symmetry in quantum systems tied to hidden information

Yu-Jie Liu of Technical University of Munich and colleagues have linked the emergence of 1-form symmetries in quantum systems to the preservation of information about a system’s underlying structure. The work demonstrates that these symmetries, which act on sub-dimensional spatial manifolds, can appear even when explicitly broken at the microscopic level, presenting a challenge to traditional symmetry analysis. Researchers analytically determined the conditions for 1-form symmetry emergence in product states on one- and two-dimensional lattices, and developed a method to detect these symmetries using a quantum error correction decoder. The findings suggest a connection between symmetry and information retention, revealing an information-theoretic transition detectable through long-range entanglement. The existence of an emergent 1-form symmetry can be determined by examining the recoverable information about a microscopic, or “bare”, symmetry within a quantum system. This work proposes that these symmetries, which manifest at low energies despite being broken at the fundamental level, are fundamentally linked to information preservation, not just the system’s inherent properties. Researchers established a criterion for identifying a 1-form symmetry in quantum states on lattice systems, even when the…