Quantum theory of measurements as quantum decision theory

23rd International Laser Physics Workshop

Yukalov, V.I.^1,2 ; Sornette, D.^2,3

Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna

141980, Russia^1

DMTEC, ETH Zürich, Swiss Federal Institute of Technology, Zürich

CH-8092, Switzerland^2

Swiss Finance Institute, C/o University of Geneva, Geneva CH-1211, Switzerland^3

关键词: Classical probabilities;    Interference terms;    Mathematical foundations;    Measuring device;    Positive operator valued measure;    Quantum measurement;    Quantum probabilities;    Theory of measurement;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/594/1/012048/pdf
DOI  :  10.1088/1742-6596/594/1/012048

来源: IOP

【 摘 要 】

Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device.