Related papers: Quantum conditional probabilities
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.…
Quantum states containing records of incompatible outcomes of quantum measurements are valid states in the tensor-product Hilbert space. Since they contain false records, they conflict with the Born rule and with our observations. I show…
The quantum nonlocality is limited by relativistic causality, however, the reason is not fully understood yet. The relativistic causality condition on nonlocal correlations has been usually accepted as a prohibition of faster-than-light…
Applications of quantum mechanics have led to many successful predictions and explanations of puzzling phenomena, and we now apply quantum mechanics to gain, process, and communicate information in novel ways. We can understand quantum…
For linear combinations of quantum product averages in an arbitrary bipartite state, we derive new quantum Bell-form and CHSH-form inequalities with the right-hand sides expressed in terms of a bipartite state. This allows us to specify in…
We study a conditional state on a quantum logic using Renyi's approach (or Bayesian principle). This approach helps us to define independence of events and differently from the situation in the classical theory of probability, if an event…
Updating a probability distribution in the light of new evidence is a very basic operation in Bayesian probability theory. It is also known as state revision or simply as conditioning. This paper recalls how locally updating a joint state…
We discuss coupling of violation of Bell's inequality and non-Kolmogorovness of statistical data in the EPR-Bohm experiment. We emphasize that nonlocalty and "death of realism" are only sufficient, but not necessary conditions of…
We propose a complete proof of the Born rule using an additional postulate stating that for a short enough time {\Delta}t between two measurements, a property of a particle will keep its values fixed. This dynamical postulate allows us to…
When a conscious observer is part of a quantum mechanical system, rule (4) cuts off solutions to the Schrodinger equation. It is important to show that this interruption of the Hamiltonian dynamics does not effect the statistical…
Without Niels Bohr, QBism would be nothing. But QBism is not Bohr. This paper attempts to show that, despite a popular misconception, QBism is no minor tweak to Bohr's interpretation of quantum mechanics. It is something quite distinct.…
It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schr\"odinger equation are derived from the causal action principle. The…
We find the conditions under which a quantum regression theorem can be assumed valid for non-Markovian master equations consisting in Lindblad superoperators with memory kernels. Our considerations are based on a generalized Born-Markov…
It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumption that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to…
Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
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…
The definition of the conditional probability is very important in the theory of the probability. This definition is based on the fact, that random events can be simultaneously measurable. This paper deal with the problem of conditioning…
We use a novel form of quantum conditional probability to define new measures of quantum information in a dynamical context. We explore relationships between our new quantities and standard measures of quantum information, such as von…
A b s t r a c t It will be argued that 1) the Bell inequalities are not equivalent with those inequalities derived by Pitowsky and others that indicate the Kolmogorovity of a probability model, 2) the original Bell inequalities are…