Related papers: New derivation of Born's law and parameter estimat…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is…
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 quantum mechanics postulate called the Born Rule attributes a probabilistic meaning to a wave function. This paper derives the Born Rule from other quantum principles along with a model of the measurement process. The nondeterministic…
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,…
I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…
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…
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…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
The paper discuss the structure of quantum mechanics and uniqueness of its postulates. The Born rule for quantum probabilities is fixed by requirement of nonexistence of quantum telepathy. Von Neumann projection postulate describes the…
The notion of probability plays a crucial role in quantum mechanics. It appears in quantum mechanics as the Born rule. In modern mathematics which describes quantum mechanics, however, probability theory means nothing other than measure…
Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations…
We deduce the Born rule. No use is required of quantum postulates. One exploits only rudimentary quantum mathematics--a linear, not Hilbert', vector space--and empirical notion of the statistical length of a state. Its statistical nature…
In a quantum-Bayesian take on quantum mechanics, the Born Rule cannot be interpreted as a rule for setting measurement-outcome probabilities from an objective quantum state. But if not, what is the role of the rule? In this paper, we argue…
The Born postulate can be reduced to its deterministic content that only applies to eigenvectors of observables: the standard probabilistic interpretation of generic states then follows from algebraic properties of repeated measurements and…
The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it…
Born's rule in its conventional textbook form applies to the small class of projective measurements only. It is well-known that a generalization of Born's rule to realistic experiments must be phrased in terms of positive operator valued…
We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that a rational decision maker behaves as if…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
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…