Related papers: Quantum Bayesianism at the Perimeter
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…
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…
A different approach towards quantum theory is proposed in this paper. The basis is taken to be conceptual variables, physical variables that may be accessible or inaccessible, i.e., it may be possible or impossible to assign numerical…
A realist description of our universe requires a twofold concept of locality. On one hand, there are the strictly Einstein-local interactions which generate the time evolution. On the other hand, the quantum state space calls for a…
The new emerging quantum physics - quantum computing conceptual bridge, mandates a ``grand unification'' of space-time-matter and quantum information (all quantized), with deep implications for science in general. The major physics…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
A new approach to the problem of measurement in quantum mechanics is proposed. In this approach, the process of measurement is described in the Heisenberg picture and divided into two stages. The first stage is to transduce the measured…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
We propose an exercise in which one attempts to deduce the formalism of quantum mechanics solely from phenomenological observations. The only assumed inputs are obtained through sequential probing of quantum systems; no presuppositions…
Considerable effort has been devoted to deriving the Born rule (e.g. that $|\psi(x)|^2 dx$ is the probability of finding a system, described by $\psi$, between $x$ and $x + dx$) in quantum mechanics. Here we show that the Born rule is not…
In this paper we attempt to analyze the concept of quantum probability within quantum computation and quantum computational logic. While the subjectivist interpretation of quantum probability explains it as a reliable predictive tool for an…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current…
A quantum mechanical theory is proposed which abandons an external parameter ``time'' in favor of a self-adjoint operator on a Hilbert space whose elements represent measurement events rather than system states. The standard quantum…
We describe a general procedure for associating a minimal informationally-complete quantum measurement (or MIC) and a set of linearly independent post-measurement quantum states with a purely probabilistic representation of the Born Rule.…
The Born rule provides a probability vector (distribution) with a quantum state for a measurement setting. For two settings, we have a pair of vectors from the same quantum state. Each pair forms a combined-probability vector that obeys…
The probabilistic rule that links the formalism of Quantum Mechanics (QM) to the real world was stated by Born in 1926. Since then, there were many attempts to derive the Born postulate as a theorem, Gleason's being the most prominent. The…