Entanglement is a defining feature of quantum physics, but not all entangled states are equal. What techniques can be used to generate maximally entangled states? Artistic impression of quantum entanglement of two atoms (Courtesy: iStock/Koto Feja) An absolutely maximally entangled (AME) state is one in which every possible division of a many-body system into two groups is as entangled as quantum mechanics allows. This makes AME states uniquely valuable as benchmarks for quantum theory and as resources for quantum technologies. Yet basic questions about their existence, structure and classification have remained unresolved, even after two decades of study. In a new work, dedicated to Ryszard Horodecki, this field has been advanced in several important ways. First, the authors provided a comprehensive and up to date overview of known methods for constructing AME states, going beyond traditional approaches based on stabilizer and graph states.…