University of Pavia, Italy, paolo.perinotti@unipv.it
(joint work with Giacomo Mauro D’Ariano and Alessandro Tosini)
The origin of many counterintuitive features of quantum theory is complementarity, by which we mean the existence of measurements that are mutually exclusive: if an observer performs one measurement on a given system, he will not be able to know what would have happened had he chosen to perform a complementary one. This fact, in turn, is strictly linked to the impossibility of extracting relevant information from a given system without irretrievably affecting the outcomes of any subsequent measurement, as quintessentially described in Heisenberg?s account of the gamma ray microscope thought experiment. The principle of No-information without disturbance will be discussed here in the context of general Operational Probabilistic Theories (OPTs)?a class of theories ruling the processes of hypothetical elementary systems, playing the role of foils or candidate alternatives to classical or quantum systems for physics, as well as their probabilities. This approach allows one to understand the features of quantum mechanics in a deeper way, distinguishing what phenomena are genuinely quantum, and what are typical of most theories. We will show necessary and sufficient conditions for no information without disturbance, dis- cussing their operational interpretation. We will also illustrate the geometric features of a state space that embody the possibility or impossibility to extract information without disturbance. Particular care is taken in the definition of disturbance, considering not only direct disturbance on the system undergoing the measurement, i.e. on statistics of other measurements, but also on correlations with external systems. The role of composition rules will be highlighted, illustrating the unexpected features of theories without local discriminability in this respect. All the results will be proved without assuming causality, which implies that disturbance can affect both preceding and subsequent measurements.
[1] G. M. D’Ariano, P. Perinotti, A. Tosini, Information and disturbance in operational probabilistic theories, arXiv:1907.07043.