Related papers: Representation theorem for obsevables on a quantum…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…
Quantum theory predicts probabilities as well as relative phases between different alternatives of the system. A unified description of both probabilities and phases comes through a generalisation of the notion of a density matrix for…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
Contextuality is one way of capturing the non-classicality of quantum theory. The contextual nature of a theory is often witnessed via the violation of non-contextuality inequalities---certain linear inequalities involving probabilities of…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
In this paper, epistemology and ontology of quantum states are discussed based on a completely new way of founding quantum theory. The fundamental notions are conceptual variables in the mind of an observer or in the joint minds of a group…
In the theory of classical statistical inference one can derive a simple rule by which two or more observers may combine {\em independently} obtained states of knowledge together to form a new state of knowledge, which is the state which…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Let Alice and Bob be able to make local quantum measurements and communicate classically. The set of mathematically consistent joint probability assignments (``states'') for such measurements is properly larger than the set of…
In classical physics the joint probability of a number of individually rare independent events is given by the Poisson distribution. It describes, for example, unidirectional transfer of population between the densely and sparsely populated…
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…
Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This…
In this work we first propose to exploit the fundamental properties of quantum physics to evaluate the probability of events with projection measurements. Next, to study what events can be specified by quantum methods, we introduce the…
Can the state-space of $d$-dimensional quantum theory be derived from studying the behavior of a single "reference" measuring device? The answer is yes, if the measuring device corresponds to a complex-projective 3-design. In this…
We study asymptotically optimal statistical inference concerning the unknown state of $N$ identical quantum systems, using two complementary approaches: a "poor man's approach" based on the van Trees inequality, and a rather more…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…
We introduce a new concept called as the mutual uncertainty between two observables in a given quantum state which enjoys similar features like the mutual information for two random variables. Further, we define the conditional uncertainty…
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…