Researchers have developed a new concept to quantify the dimensionality of entanglement in multiparticle quantum systems. Although entanglement is a crucial resource for quantum technologies, especially in complex systems with multiple particles or higher dimensions, the interplay between dimensionality and multiparticle entanglement was not well understood. Until now, only a clear notion of entanglement dimensionality existed for two-particle systems, based on the Schmidt decomposition.

The new approach introduces the concept of "partition rank," which characterizes the entanglement dimensionality of multiparticle quantum states. This is based on decomposing pure states into superpositions of states without genuine multiparticle entanglement. The authors have provided constructive methods to determine this partition rank for both pure and mixed states. This advance allows for the identification of novel maximally correlated states and offers a discrete classification of quantum states under stochastic local operations and classical communication (SLOCC).

From a mathematical perspective, the proposed methodology is formulated in terms of the slice rank and partition rank of tensors. The obtained results allow for the characterization of these metrics by connecting them to a generalized injective tensor norm. This work opens new avenues for understanding and manipulating entanglement in complex quantum systems, which is fundamental for the development of quantum computing and communications.