A new study has developed a majorization theory for quantum quasiprobability distributions, providing a unified framework to understand and quantify non-classicality in quantum systems. This approach allows for the comparison of different quantum states and operations in terms of their "quantumness," i.e., their deviation from classical models. Majorization, a mathematical tool that compares the spread of two distributions, is extended here to characterize the inherent non-classical nature of these quasiprobability functions, which are fundamental for describing quantum states in phase space.

Traditionally, non-classicality has been assessed using specific metrics often focused on a particular aspect, such as the presence of negative values in the Wigner function or the violation of Bell inequalities. Majorization theory offers a more general perspective, allowing the establishment of hierarchies between quantum states and operations based on their degree of non-classicality. This is crucial for identifying valuable quantum resources for computation and metrology, as well as for understanding the limits of classical simulation of quantum phenomena.

This unified framework not only consolidates previous results but also opens new avenues for the design of quantum experiments and algorithms. By providing a rigorous way to compare the "quantumness" of different systems, majorization theory can guide the search for optimal states for specific tasks, such as fault-tolerant quantum computing or the detection of extremely weak signals. Furthermore, it could shed light on how non-classicality degrades under decoherence, a central challenge in the development of quantum technologies.