Quantum Probabilities of Composite Events in Quantum Measurements With Multimode States

Laser Physics, Vol. 23, p. 105502, 2013

28 Pages Posted: 28 Aug 2013

See all articles by Vyacheslav I. Yukalov

Vyacheslav I. Yukalov

Joint Institute for Nuclear Research; D-MTEC, ETH Zurich

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech); Swiss Finance Institute; ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Tokyo Institute of Technology

Date Written: August 27, 2013

Abstract

The problem of defining quantum probabilities of composite events for quantum decision theory and theory of quantum measurements is considered. These theories not merely are closely related with each other, but decision theory, actually, can be treated as a part of measurement theory. We show that the Luders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint probability. We suggest the definition of quantum joint probabilities by introducing composite events in multichannel measurements. The notion of measurements under uncertainty is defined. We demonstrate that the necessary condition for the mode interference is the entanglement of the composite prospect together with the entanglement of the composite statistical state. As an illustration, we consider an example of a quantum game. A special attention is payed to the application of the approach to systems with multimode states. The measurement of composite events including multimode states corresponds to the measurement under uncertainty, which is equivalent to decision making under uncertainty.

Suggested Citation

Yukalov, Vyacheslav I. and Sornette, Didier, Quantum Probabilities of Composite Events in Quantum Measurements With Multimode States (August 27, 2013). Laser Physics, Vol. 23, p. 105502, 2013 , Available at SSRN: https://ssrn.com/abstract=2316701

Vyacheslav I. Yukalov (Contact Author)

Joint Institute for Nuclear Research ( email )

Bogolubov Laboratory of Theoretical Physics
Dubna, 141980
Russia

D-MTEC, ETH Zurich ( email )

Zurich
Switzerland

Didier Sornette

Risks-X, Southern University of Science and Technology (SUSTech) ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Tokyo Institute of Technology ( email )

2-12-1 O-okayama, Meguro-ku
Tokyo 152-8550, 52-8552
Japan

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