Related papers: Quantum(-like) decision making: on validity of the…
We present a general theory of quantum information processing devices, that can be applied to human decision makers, to atomic multimode registers, or to molecular high-spin registers. Our quantum decision theory is a generalization of the…
Following Frauchiger and Renner's discovery of a conflict between quantum mechanics and certain commonsense reasoning axioms, much work has gone into finding alternative axiomatizations that can avoid the conflict. However, this body of…
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…
The cognitive state of mind concerning a range of choices to be made can effectively be modelled in terms of an element of a high-dimensional Hilbert space. The dynamics of the state of mind resulting form information acquisition is…
Recently the mathematical formalism of quantum mechanics, especially methods of quantum probability theory, started to be widely used in a variety of applications outside of physics, e.g., cognition and psychology as well as economy and…
A quantum state can be understood in a loose sense as a map that assigns a value to every observable. Formalizing this characterization of states in terms of generalized probability distributions on the set of effects, we obtain a simple…
It has been suggested, on the one hand, that quantum states are just states of knowledge; and, on the other, that quantum theory is merely a theory of correlations. These suggestions are confronted with problems about the nature of…
The standard argument for the validity of Einstein's equivalence principle in a non-relativistic quantum context involves the application of a mass superselection rule. It is surprising that the consistency between such an important…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that a rational decision maker behaves as if…
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a…
The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social…
In classical statistical decision theory, comparison of experiments plays very important role. Especially, so-called randomization criteria is most important. In this paper, we establish two kinds of quantum analogue these concepts, and…
Quantum cognition in decision-making is a recent and rapidely growing field. In this paper we develop an expected utility theory in a context of non-classical (quantum) uncertainty. We replace the classical state space with a Hilbert space…
Analogies between quantum mechanics and sociology lead to the hypothesis that quantum objects are complex products of evolution. Like biological objects they are able to receive, to work on, and to spread semantic information. In general…
It is always possible to decide, with one-sided error, whether two quantum states are the same under a specific unitary transformation. However we show here that it is {\em impossible} to do so if the transformation is anti-linear and…
Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental…
Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This…