Dynamic consistency of expected utility under non-classical (quantum) uncertainty

Targeting in quantum persuasion problem

“…It is intuitively clear that if the states B and T are close to each other then the probability p for the transition B → T can be made close to 1. Conversely, in [8] we proved that if p is close to 1 then the states B and T are close as well. On the other hand, the probability p can vanish.…”

“…An important feature of the quantum situation is that this relation is probabilistic: the state of the system only defines the probabilities for the different outcomes. We represent MD M as follows 7 A behavioral justification for this rule is provided in [8]. And in [3] Lüders rule is shown to be a direct generalization of Bayes rule.…”

“…In our quantum context, we need to consider compound MDs because the composition of two (or more) noncommuting measurements is not a projective measurement. 8 We now introduce the possibility that the outcomes of the measurement are not di- Definition. An information structure (IS) is a MD (with a set I of outcomes) together…”

Preparing a (quantum) belief system

“…In fact for any Hermitian operator A and state B we can define the 'expected value' of A in state B as Tr(AB). In [6] it is shown that a decision(action) subject to non-classical uncertainty that is an action whose consequence depends on the uncertain state of Quantum measurements be they direct or more general are characterized by a few distinguishing features. Most importantly, the performance of a measurement impacts on the state of the system.…”

“…Let H be a two-dimensional Hilbert space with an orthonormal basis (e 1 , e 2 ) and let (P 1 , P 2 ) be the corresponding projectors. Following [6], the utility of the smartphone is expressed as operator A which gives a utility equal to 100 in state |e 1 (the smartphone is Excellent) and 0 in |e 2 (the smartphone is . 3 This means that the (|e 1 , |e 2 ) and (|G , |N G ) are two properties (perspectives) that are incompatible in the mind of Receiver.…”