Related papers: Logical independence and quantum randomness
Quantum theory can be viewed as a generalization of classical probability theory, but the analogy as it has been developed so far is not complete. Whereas the manner in which inferences are made in classical probability theory is…
According to a recent no-go theorem (M. Pusey, J. Barrett and T. Rudolph, Nature Physics 8, 475 (2012)), models in which quantum states correspond to probability distributions over the values of some underlying physical variables must have…
Propositional team logic is the propositional analog to first-order team logic. Non-classical atoms of dependence, independence, inclusion, exclusion and anonymity can be expressed in it, but for all atoms except dependence only exponential…
We discuss how to reconstruct quantum theory from operational postulates. In particular, the following postulates are consistent only with for classical probability theory and quantum theory. Logical Sharpness: There is a one-to-one map…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
For a two-particle two-state system, sets of compatible propositions exist for which quantum mechanics and noncontextual hidden-variable theories make conflicting predictions for every individual system whatever its quantum state. This…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Quantum correlations, like entanglement, represent the characteristic trait of quantum mechanics, and pose essential issues and challenges to the interpretation of this pillar of modern physics. Although quantum correlations are largely…
We show how G\"odel's first incompleteness theorem has an analog in quantum theory. G\"odel's theorem implies endless opportunities for appending axioms to arithmetic, implicitly showing a role for an agent, namely an agent that asserts an…
We show that quantum information can be encoded into entangled states of multiple indistinguishable particles in such a way that any inertial observer can prepare, manipulate, or measure the encoded state independent of their Lorentz…
I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…
Quantum theory demands that, in contrast to classical physics, not all properties can be simultaneously well defined. The Heisenberg Uncertainty Principle is a manifestation of this fact. Another important corollary arises that there can be…
We apply the causal interpretation of quantum mechanics to homogeneous quantum cosmology and show that the quantum theory is independent of any time-gauge choice and there is no issue of time. We exemplify this result by studying a…
We consider the problem of determining the state of a quantum system given one or more readings of the expectation value of an observable. The system is assumed to be a finite dimensional quantum control system for which we can influence…
The notion of "closed systems" in Quantum Mechanics is discussed. For this purpose, we study two models of a quantum-mechanical system $P$ spatially far separated from the "rest of the universe" $Q$. Under reasonable assumptions on the…
In Bell scenario, any nonlocal correlation, shared between two spatially separated parties, can be modeled deterministically either by allowing communications between the two parties or by restricting their free will in choosing the…
It is known that the global state of a composite quantum system can be completely determined by specifying correlations between measurements performed on subsystems only. Despite the fact that the quantum correlations thus suffice to…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…