Related papers: Measures and their random reals
We consider the motion of a quantum particle whose position is measured in random places at random moments in time. We contrast this motion with the motion of a quantum particle in a potential which varies randomly in space and in time,…
Nies and Scholz introduced the notion of a state to describe an infinite sequence of qubits and defined quantum-Martin-Lof randomness for states, analogously to the well known concept of Martin-L\"of randomness for elements of Cantor space…
This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set…
We establish connections between the requirement of measurability of a probability space and the principle of complimentarity in quantum mechanics. It is shown that measurability of a probability space implies the dependence of results of…
In this paper we study a class of random Cantor sets. We determine their almost sure Hausdorff, packing, box, and Assouad dimensions. From a topological point of view, we also compute their typical dimensions in the sense of Baire category.…
Quantum measurement is universal for quantum computation. This universality allows alternative schemes to the traditional three-step organisation of quantum computation: initial state preparation, unitary transformation, measurement. In…
Randomness is intrinsic to quantum mechanics; the outcome of a measurement on a quantum state is a random variable. This feature has been applied to randomness certification, where one party must decide whether the data they receive is…
The question whether quantum measurements reflect some underlying objective reality has no generally accepted answer. We show that description of such reality is possible under natural conditions such as linearity and causality, although in…
A general theory of resource-bounded measurability and measure is developed. Starting from any feasible probability measure $\nu$ on the Cantor space $\C$ and any suitable complexity class $C \subseteq \C$, the theory identifies the subsets…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
In quantum theory, it is known for a pair of noncommutative observables that there is no state on which they take simultaneously definite values, and that there is no joint measurement of them. They are called preparation uncertainty and…
A circle, centered at the origin and with radius chosen so that it has non-empty intersection with the integer lattice $\mathbb{Z}^{2}$, gives rise to a probability measure on the unit circle in a natural way. Such measures, and their weak…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
We propose a protocol to test whether the postulate of a measurement acting as an instantaneous projection onto an eigenstate of the measurement apparatus is compatible with physical reality. This approach is solely based on repeated…
Given an ontological model of a quantum system, a "genuine measurement," as opposed to a quantum measurement, means an experiment that determines the value of a beable, i.e., of a variable that, according to the model, has an actual value…
The low for random reals are characterized topologically, as well as in terms of domination of Turing functionals on a set of positive measure.
We describe in a qualitative way a possible picture of the Measurement Process in Quantum Mechanics, which takes into account: 1. the finite and non zero time duration T of the interaction between the observed system and the microscopic…
The problem of measurement in quantum mechanics is reanalyzed within a general, strictly probabilistic framework (without reduction postulate). Based on a novel comprehensive definition of measurement the natural emergence of objective…