Related papers: Derivation of quantum probability from measurement
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
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…
Understanding the core content of quantum mechanics requires us to disentangle the hidden logical relationships between the postulates of this theory. Here we show that the mathematical structure of quantum measurements, the formula for…
The Born probability measure describes the statistics of measurements in which observers self-locate themselves in some region of reality. In $\psi$-ontic quantum theories, reality is directly represented by the wavefunction. We show that…
We consider the probability by which quantum phase measurements of a given precision can be done successfully. The least upper bound of this probability is derived and the associated optimal state vectors are determined. The probability…
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…
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…
From an analysis of projective measurements, it is shown that the Wigner rule is the unique operational quasi-probability for the post-measurement state. A unique pre-measurement quasi-probability is derived from a principle of invariance…
Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
The additivity of classical probabilities is only the first in a hierarchy of possible sum-rules, each of which implies its successor. The first and most restrictive sum-rule of the hierarchy yields measure-theory in the Kolmogorov sense,…
The measurement postulate of quantum theory stands in conflict with the laws of thermodynamics and has evoked debate regarding what actually constitutes a measurement. With the help of modern quantum statistical mechanics, we take the first…
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…
The Born rule for probabilities of measurement results is deduced from the set of five assumptions. The assumptions state that: (a) the state vector fully determines the probabilities of all measurement results; (b) between measurements,…
In the first part of this two-part article, we have introduced and analyzed a multidimensional model, called the 'general tension-reduction' (GTR) model, able to describe general quantum-like measurements with an arbitrary number of…
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…
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…
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…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
After a brief review of classical probability theory (measure theory), we present an observation (due to Sorkin) concerning an aspect of probability in quantum mechanics. Following Sorkin, we introduce a generalized measure theory based on…