Decoherence and equilibration under nondestructive measurements

Sornette

2016

Front. Phys.

We give a mathematical definition for the notion of inconclusive quantum measurements. In physics, such measurements occur at intermediate stages of a complex measurement procedure, with the final measurement result being operationally testable. Since the mathematical structure of Quantum Decision Theory (QDT) has been developed in analogy with the theory of quantum measurements, the inconclusive quantum measurements correspond, in QDT, to intermediate stages of decision making in the process of taking decisions under uncertainty. The general form of the quantum probability for a composite event is the sum of a utility factor, describing a rational evaluation of the considered prospect, and of an attraction factor, characterizing irrational, subconscious attitudes of the decision maker. Despite the involved irrationality, the probability of prospects can be evaluated. This is equivalent to the possibility of calculating quantum probabilities without specifying hidden variables. We formulate a general way of evaluation, based on the use of non-informative priors. As an example, we suggest the explanation of the decoy effect. Our quantitative predictions are in very good agreement with experimental data.

Section: Composite Quantum Measurements and Eventsmentioning

confidence: 99%

Inconclusive Quantum Measurements and Decisions under Uncertainty

Sornette

2016

Front. Phys.

“…Any real measurement requires finite time and involves interactions with measuring devices and observers [6,[36][37][38][39]. Even the so-called nondemolition and nondestructive measurements may essentially influence the measured system [40][41][42][43]. In what follows, the environment, including measuring apparatuses and observers, acting on the system in the process of measurement, will be called for short a measurer.…”

Section: Quantum State Reductionmentioning

confidence: 99%

Quantum probabilities of composite events in quantum measurements with multimode states

Sornette

2013

Laser Phys.

The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that the Lüders 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 multi-mode states, such as atoms, molecules, quantum dots, or trapped Bose-condensed atoms with several coherent modes.

“…It is easy to show that the Lappo-Danilevsky condition ( 12 ) is equivalent to the validity of eigenproblem ( 14 ) with time-independent eigenfunctions. Exactly the same situation happens in quantum theory in the case of nondestructive or nondemolition measurements [ 29 , 30 , 31 , 32 , 33 , 34 , 35 ].…”

Section: Single Decision Makingmentioning

confidence: 73%

Evolutionary Processes in Quantum Decision Theory

2020

Entropy

The review presents the basics of quantum decision theory, with an emphasis on temporary processes in decision making. The aim is to explain the principal points of the theory. How an operationally-testable, rational choice between alternatives differs from a choice decorated by irrational feelings is elucidated. Quantum-classical correspondence is emphasized. A model of quantum intelligence network is described. Dynamic inconsistencies are shown to be resolved in the frame of the quantum decision theory.