What kind of dynamic decision process do humans use to make decisions? In this article, two different types of processes are reviewed and compared: Markov and quantum. Markov processes are based on the idea that at any given point in time a decision maker has a definite and specific level of support for available choice alternatives, and the dynamic decision process is represented by a single trajectory that traces out a path across time. When a response is requested, a person's decision or judgment is generated from the current location along the trajectory. By contrast, quantum processes are founded on the idea that a person's state can be represented by a superposition over different degrees of support for available choice options, and that the dynamics of this state form a wave moving across levels of support over time. When a response is requested, a decision or judgment is constructed out of the superposition by "actualizing" a specific degree or range of degrees of support to create a definite state. The purpose of this article is to introduce these two contrasting theories, review empirical studies comparing the two theories, and identify conditions that determine when each theory is more accurate and useful than the other. This article is categorized under: Economics > Individual Decision-Making Psychology > Reasoning and Decision Making Psychology > Theory and Methods.
We review the basic concepts of quantum stochastics using the universal Itô *-algebra approach.The main notions and results of classical and quantum stochastics are reformulated in this unifying approach.The thermal quantum Lévy process with commuting increments is defined in terms of the modular *-Itô algebra.The quasi-Markov quantum stochastic processes over increasing W*-algebras generated by a quantum Lévy process is characterized in terms of their quantum stochastic germs.The corresponding quantum stochastic master equation on the increasing predual L-spaces is derived as a noncommutative and non-Markov generalization of the Zakai equation driven by the dual quantum Lévy process.This is done by a noncommutative analog of the Girsanov transformation which we introduce here in full generality.
We demonstrate that
k-Markov sequences of unitary gates provide low-cost handles to manipulate the rate and structure of information spreading compared to traditional random, 0-Markov, circuits. For SWAP gates and brickwork circuits, we use graph cover time to demonstrate how
k-Markov processes can be used to control operator transport. With SWAP gates and the set of Clifford gates that can change operator weight, we show how
k-Markov sequences can be used to manipulate scrambling time and generate novel structures of spatial-temporal correlations across a qubit network. We show that
k-Markov circuits constructed from PSWAP gates at fixed angle are equivalent to standard brickwork circuits with PSWAP angle drawn from non-uniform distributions generated by the
k-Markov process. In those circuits, the time evolution of the average Hamming weight and the space-time correlation structure that remains after one-point quantities equilibrate again vary significantly from the 0-Markov case, depending on the transition probabilities of the process. More broadly, these results identify finite temporal memory as a control handle distinct from a circuit's degree of quantum chaos. For gate sets that fall short of volume-law scrambling, the equilibrium reached by one-point diagnostics is fixed by the gates alone, while the choice of
k-Markov rule controls the approach to equilibrium and the structure of persistent, late-time correlations.