Related papers: Quantum Interval-Valued Probability: Contextuality…
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…
Near-term quantum computation holds potential across multiple application domains. However, imperfect preparation and evolution of states due to algorithmic and experimental shortcomings, characteristic in the near-term implementation,…
Physical entities are ultimately (re)constructed from elementary yes/no events, in particular clicks in detectors or measurement devices recording quanta. Recently, the interpretation of certain such clicks has given rise to unfounded…
Page has recently argued that the Born rule does not suffice for computing all probabilities in quantum cosmology. He further asserts that the Born rule's failure gives rise to the cosmological measure problem. Here I contend that Page's…
We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are…
This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the…
The Kochen-Specker theorem proves the inability to assign, simultaneously, noncontextual definite values to all (of a finite set of) quantum mechanical observables in a consistent manner. If one assumes that any definite values behave…
In this paper we attempt to analyze the physical and philosophical meaning of quantum contextuality. We will argue that there exists a general confusion within the foundational literature arising from the improper "scrambling" of two…
It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos…
Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S^2, can be colored so that the contradiction with hidden…
Modal interpretations have the ambition to construe quantum mechanics as an objective, man-independent description of physical reality. Their second leading idea is probabilism: quantum mechanics does not completely fix physical reality but…
Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits to the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
Quantum contextuality is a concept used to describe the property of hidden-variable theory that measurement outcomes predetermined by the hidden variables depend on the measurement context. The term measurement context can have different…
We consider the possibility that the relative phase in quantum mechanics plays a role in determining measurement outcome and could therefore serve as a "hidden" variable. The Born rule for measurement equates the probability for a given…
Realist, no-collapse interpretations of quantum mechanics, such as Everett's, face the probability problem: how to justify the norm-squared (Born) rule from the wavefunction alone. While any basis-independent measure can only be…
We investigate the consistency of conditional quantum probabilities. This is whether there is compatibility between the Kolmogorov-Bayes conditional probabilities and the Born rule. We show that they are not compatible in the sense that…
The interpretation of quantum mechanics has been a problem since its founding days. A large contribution to the discussion of possible interpretations of quantum mechanics is given by the so-called impossibility proofs for hidden variable…
There are two powerful arguments against the possibility of extending quantum mechanics, the violation of Bell inequalities and the Kochen-Specker theorem, but the connection between the two remains confused. Following the distinctive…
In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum…