Related papers: Logical independence and quantum randomness
Although randomization has long been used in distributed computing, formal methods for reasoning about probabilistic concurrent programs have lagged behind. No existing program logics can express specifications about the full distributions…
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…
According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the…
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates.…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…
A new interpretation of quantum mechanics is proposed according to which precedence, freedom and novelty play central roles. This is based on a modification of the postulates for quantum theory given by Masanes and Muller. We argue that…
In R.D. Sorkin's framework for logic in physics a clear separation is made between the collection of unasserted propositions about the physical world and the affirmation or denial of these propositions by the physical world. The unasserted…
This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based…
Due to the absence of an external, classical time variable, the probabilistic predictions of covariant quantum theory are ambiguous when multiple measurements are considered. Here, we introduce an information theoretic framework to the…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
Elementary particles in quantum mechanics (QM) are indistinguishable when sharing the same intrinsic properties and the same quantum state. So, we can consider quantum particles as non-individuals, although non-individuality is usually…
The analyzability of the universe into subsystems requires a concept of the "independence" of the subsystems, of which the relativistic quantum world supports many distinct notions which either coincide or are trivial in the classical…
We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different…
When conducting a Bell test, it is normal to assume that the preparation of the quantum state is independent of the measurements performed on it. Remarkably, the violation of local realism by entangled quantum systems can be certified even…
Bayesian networks provide a powerful tool for reasoning about probabilistic causation, used in many areas of science. They are, however, intrinsically classical. In particular, Bayesian networks naturally yield the Bell inequalities.…
Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce $\textit{collective}$ randomized…
We give a purely logical proof of the J. Conway and S. Kochen Free Will theorem concerning undeterminacy in Quantum Mechanics (Notices of the AMS, February 2009, Vol. 56/2, p. 226). The logical method seems to be very powerful.
We derive exceedingly simple practical procedures revealing the quantum nature of states and measurements by the violation of classical upper bounds on the statistics of arbitrary measurements. Data analysis is minimum and definite…