Related papers: Conditional expectation and Bayes' rule for quantu…
We show that the correct mathematical foundation of quantum decision theory, dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of the projection-valued measure. The latter is…
It is well-established that quantum probability does not follow classical Kolmogorov probability calculus. Various approaches have been developed to loosen the axioms, of which the use of signed measures is the most successful (e.g. the…
In the quantum-Bayesian approach to quantum foundations, a quantum state is viewed as an expression of an agent's personalist Bayesian degrees of belief, or probabilities, concerning the results of measurements. These probabilities obey the…
Quantum measurement and quantum operation theory is developed here by taking the relational properties among quantum systems, instead of the independent properties of a quantum system, as the most fundamental elements. By studying how the…
We consider the possibility that the relative phase in quantum mechanics plays a role in determining measurement outcome and could therefore serve as a "hidden" variable. The Born rule for measurement equates the probability for a given…
It has been recently suggested that probabilities of different events in the multiverse are given by the frequencies at which these events are encountered along the worldline of a geodesic observer (the "watcher"). Here I discuss an…
An understanding of quantum theory in terms of new, underlying descriptions capable of explaining the existence of non-classical correlations, non-commutativity of measurements and other unique and counter-intuitive phenomena remains still…
An extension of the conditional expectations (those under a given subalgebra of events and not the simple ones under a single event) from the classical to the quantum case is presented. In the classical case, the conditional expectations…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…
In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…
Contrary to general relativity, quantum theory treats space and time in fundamentally different ways. In particular, while joint probabilities associated with spacelike separated measurements are defined in terms of the Born rule, joint…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
The conventional postulate for the probabilistic interpretation of quantum mechanics is asymmetric in preparation and measurement, making retrodiction reliant on inference by use of Bayes' theorem. Here, a more fundamental symmetric…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
We begin with a study of operations and the effects they measure. We define the probability that an effect $a$ occurs when the system is in a state $\rho$ by $P_\rho (a)= tr(\rho a)$. If $P_\rho (a)\ne 0$ and $\mathcal{I}$ is an operation…