Related papers: Can the present be the average of the future?
In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…
The Born rule is part of the collapse axiom in the standard version of quantum theory, as presented by standard textbooks on the subject. We show here that its signature quadratic dependence follows from a single additional physical…
Everett's Relative State Interpretation has gained increasing interest due to the progress of understanding the role of decoherence. In order to fulfill its promise as a realistic description of the physical world, two postulates are…
We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the…
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,…
Despite the tremendous empirical success of quantum theory there is still widespread disagreement about what it can tell us about the nature of the world. A central question is whether the theory is about our knowledge of reality, or a…
The apparent random outcome of a quantum measurement is conjectured to be fundamentally determined by the microscopic state of the macroscopic measurement apparatus. The apparatus state thus plays the role of a hidden variable which, in…
Modifications of quantum mechanics are considered, in which the state vector of any system, large or small, undergoes a stochastic evolution. The general class of theories is described, in which the probability distribution of the state…
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…
In the Quantum-Bayesian interpretation of quantum theory (or QBism), 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…
It is argued from several points of view that quantum probabilities might play a role in statistical settings. New approaches toward quantum foundations have postulates that appear to be equally valid in macroscopic settings. One such…
We generalize Bell's hidden variable model describing the singlet state of a two-qubits system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for…
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 amplitudes, Born rule,…
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…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
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…
The Pusey-Barrett-Rudolph theorem (PBR) claims to rule out the possibility of a purely statistical interpretation of the quantum state under an assumption of how to represent independent operations in any hidden variable model. We show that…
A hidden variables model complying with the simplest form of Local Realism was recently introduced, which reproduces Quantum Mechanics' predictions for an even ideally perfect Bell's experiment. This is possible thanks to the use of a…
In order to make the quantum mechanics a closed theory one has to derive the Born rule from the first principles, like the Schroedinger equation, rather than postulate it. The Born rule was in certain sense derived in several articles, e.g.…
Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. It is postulated that a quantum…