Classical Dual States and Quantum Theory Through Minimal Group Representation

In the article titled “Classical (ontological) dual states in quantum theory and the minimal group representation Hilbert space,” published in 2025, the authors investigate how aspects of Quantum theory can be understood through a classical lens by identifying dual classical states within it. These states, often referred to as “ontological” or even “hidden” variables, are reframed not as elusive but as explicit dual classical states reflecting a fundamental classical-quantum duality inherent in Nature. By applying the framework of the Minimal Group Representation—specifically the Mp(2) group—the authors demonstrate that the quantum system can be transformed or “classicalized” into a representation that preserves this duality symmetry. This approach situates quantum phenomena within a broader symmetry context, enabling a rigorous mathematical characterization of when and how quantum systems manifest classical features. The result is a Hilbert space representation that bridges the conceptual gap by revealing classical structures underpinning quantum descriptions.

From a quantum governance perspective, this validation of classical-quantum duality through minimal group representation offers profound implications for designing and managing quantum technologies and policies. Understanding that quantum states can be expressed as dual classical states provides a framework for interpreting quantum data and algorithms with classical analogs, facilitating the integration of quantum systems into existing classical infrastructures. The Mp(2) symmetry group serves as a foundational principle for governance frameworks that must address the seamless transition between classical and quantum realms, especially in regulatory oversight and system interoperability. Policymakers and managers can leverage this duality to establish standards ensuring quantum devices operate within predictable dual-state behaviors, thereby enhancing reliability and transparency. Furthermore, this representation could inform governance strategies related to quantum cybersecurity, error correction, and resource management by providing a formalism to monitor and control quantum-classical interfaces, ensuring that quantum advancements align with stable, classical governance paradigms.