General probabilistic theories for quantum foundations and quantum information

Guccione, J Salvadore

Teiko Heinosaari, Leevi Leppäjärvi, Martin Plávala

Andrei Yu. Khrennikov, Bourama Toni

Yuuya Yoshida, Hayato Arai, Masahito Hayashi

As a modern approach for the foundation of quantum theory, existing studies of general probabilistic theories gave various models of states and measurements that are quite different from quantum theory. In this Letter, to seek a more realistic situation, we investigate models approximately close to quantum theory. We define larger measurement classes that are smoothly connected with the class of POVMs via a parameter, and investigate the performance of perfect discrimination. As a result, we give a sufficient condition of perfect discrimination, which shows a significant improvement beyond the class of POVMs.

Gen Kimura, Junji Ishiguro, Makoto Fukui

General probabilistic theories are designed to provide operationally the most general probabilistic models including both classical and quantum theories. In this paper, we introduce a systematic method to construct a series of entropies, all of which generalize Shannon entropy in classical systems and von Neumann entropy in quantum systems. Using these entropies, the Holevo bound, an upper bound of the accessible information from a quantum system, is generalized to hold in any general probabilistic theory.

Koki Ono, Shun Umekawa, Hiroyasu Tajima

Generalized probabilistic theories (GPTs) provide a unified framework for describing probabilistic physical theories, encompassing classical and quantum theories as well as hypothetical theories beyond quantum mechanics. Since most GPTs are highly unrealistic and far removed from known physical theories, it is important to constrain them by physically reasonable principles. One of the most important such principles is consistency with thermodynamics, which has been extensively studied through toy models involving semipermeable membranes (SPMs) implementing measurements. On the other hand, information thermodynamics, which plays a central role in understanding the relationship between measurement and thermodynamics in classical and quantum theory, has remained largely undeveloped in GPTs. In this work, we construct information thermodynamics in GPTs and provide a unified framework for analyzing the relationship between measurement, feedback, information erasure, and the second law of thermodynamics. We also formulate a general framework for SPM models and analyze the thermodynamic cost of measurements implemented by SPMs. As a result, we show that no work can be extracted in contradiction with the second law as long as the measurement processes are consistent with entropy nondecrease, and derive sufficient conditions for this property for several entropy definitions proposed in GPTs. Moreover, by considering measurement processes violating these conditions, we construct explicit GPT systems realizing isothermal SPM cycles from which positive work can be extracted. These results demonstrate that violations of the second law can arise from the lack of fundamental entropy properties or discrepancies between entropy definitions, and provide a unified and model-independent foundation for understanding the relationship between thermodynamics and measurement in GPTs.