CLASSICAL & QUANTUM REVERSE PROCESSES THROUGH BAYESIAN INFERENCE

M. ASANO, Irina Basieva, Andrei Yu. Khrennikov +2 more

Bob Coecke, Robert W. Spekkens

Uwe Franz

We show how classical Markov processes can be obtained from quantum Lévy processes. It is shown that quantum Lévy processes are quantum Markov processes, and sufficient conditions for restrictions to subalgebras to remain quantum Markov processes are given. A classical Markov process (which has the same time-ordered moments as the quantum process in the vacuum state) exists whenever we can restrict to a commutative subalgebra without losing the quantum Markov property.8 Several examples, including the Azéma martingale, with explicit calculations are presented. In particular, the action of the generator of the classical Markov processes on polynomials or their moments are calculated using Hopf algebra duality.

Hans Christian von Baeyer

J. C. Lemm, J. Uhlig

Mehrdad Ashtiani, Mohammad Abdollahi Azgomi

Trust models play an important role in computational environments. One of the main aims of the work undertaken in this domain is to provide a model that can better describe the socio-technical nature of computational trust. It has been recently shown that quantum-like formulations in the field of human decision making can better explain the underlying nature of these types of processes. Based on this research, the aim of this paper is to propose a novel model of trust based on quantum probabilities as the underlying mathematics of quantum theory. It will be shown that by using this new mathematical framework, we will have a powerful mechanism to model the contextuality property of trust. Also, it is hypothesized that many events or evaluations in the context of trust can be and should be considered as incompatible, which is unique to the noncommutative structure of quantum probabilities. The main contribution of this paper will be that, by using the quantum Bayesian inference mechanism for belief updating in the framework of quantum theory, we propose a biased trust inference mechanism. This mechanism allows us to model the negative and positive biases that a trustor may subjectively feel toward a certain trustee candidate. It is shown that by using this bias, we can model and describe the exploration versus exploitation problem in the context of trust decision making, recency effects for recently good or bad transactions, filtering pessimistic and optimistic recommendations that may result in good-mouthing or bad-mouthing attacks, the attitude of the trustor toward risk and uncertainty in different situations and the pseudo-transitivity property of trust. Finally, we have conducted several experimental evaluations in order to demonstrate the effectiveness of the proposed model in different scenarios.