On properties of correlations in quantum mechanics and generalized probabilistic theories

Matthias Kleinmann, Tobias J. Osborne, Volkher B. Scholz +1 more

What singles out quantum mechanics as the fundamental theory of nature? Here we study local measurements in generalized probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalization of Dvoretzky's theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.

Richard Healey

C. T. K. Chari

Mirjam Weilenmann, Roger Colbeck

Self-testing usually refers to the task of taking a given set of observed correlations that are assumed to arise via a process that is accurately described by quantum theory, and trying to infer the quantum state and measurements. In other words it is concerned with the question of whether we can tell what quantum black-box devices are doing by looking only at their input-output behavior and is known to be possible in several cases. Here we introduce a more general question: is it possible to self-test a theory, and, in particular, quantum theory? More precisely, we ask whether within a particular causal structure there are tasks that can only be performed in theories that have the same correlations as quantum mechanics in any scenario. We present a candidate task for such a correlation self-test and analyze it in a range of generalized probabilistic theories (GPTs), showing that none of these perform better than quantum theory. A generalization of our results showing that all nonquantum GPTs are strictly inferior to quantum mechanics for this task would point to a new way to axiomatize quantum theory, and enable an experimental test that simultaneously rules out such GPTs.

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.

Ajoy Sen