Related papers: Logical independence and quantum randomness

Statistical independence is a notion ubiquitous in various fields such as in statistics, probability, number theory and physics. We establish the stability of independence for any pair of random variables by their corresponding Brockwell…

Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…

The groupoids description of Schwinger's picture of quantum mechanics is continued by discussing the closely related notions of composition of systems, subsystems, and their independence. Physical subsystems have a neat algebraic…

We initiate the systematic study of experimental quantum physics from the perspective of computational complexity. To this end, we define the framework of quantum algorithmic measurements (QUALMs), a hybrid of black box quantum algorithms…

We show that there exist informationally incomplete phase space observables such that the Cartesian margins are informationally equivalent with position and momentum. This shows that it is possible to reconstruct the position and momentum…

Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…

We investigate the notion of independence, which is at the basis of many, seemingly unrelated, properties of logic like Rational Monotony in non-monotonic logics, and interpolation theorems.

This work introduces Algorithmic Idealism a framework that reinterprets quantum mechanics as a computational process governed by algorithmic probability informational simplicity and utility optimization Reality is modeled as an…

Conditional independence reasoning has been shown to be helpful in the context of Bayesian nets to optimize probabilistic inference, and related techniques have been applied to speed up a number of logical reasoning tasks in boolean logic…

Free probability provides a framework for describing correlations between non-commuting observables in complex quantum systems whose Hilbert-space states follow maximum-entropy distributions. We examine the robustness of this framework…

Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard…

The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…

We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are…

The quantum state \psi is a mathematical object used to determine the probabilities of different outcomes when measuring a physical system. Its fundamental nature has been the subject of discussions since the inception of quantum theory: is…

A rigorous theory of quantum state reduction, the state change of the measured system caused by a measurement conditional upon the outcome of measurement, is developed fully within quantum mechanics without leading to the vicious circle…

We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…

We consider the first-order theory of random variables with the probabilistic independence relation, which concerns statements consisting of random variables, the probabilistic independence symbol, logical operators, and existential and…

We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that…

Let Alice and Bob be able to make local quantum measurements and communicate classically. The set of mathematically consistent joint probability assignments (``states'') for such measurements is properly larger than the set of…

The unpredictable process of state collapse caused by quantum measurements makes the generation of quantum randomness possible. In this paper, we explore the quantitive connection between the randomness generation and the state collapse and…