Related papers: Is independent choice possible?
The before-before experiment demonstrates that quantum randomness can be controlled by influences from outside spacetime, and therefore by immaterial free will. Rather than looking at quantum physics as the model for explaining free will,…
A rigorous general definition of quantum probability is given, which is valid for elementary events and for composite events, for operationally testable measurements as well as for inconclusive measurements, and also for non-commuting…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
Bell inequalities may only be derived, if hidden variables do not depend on the experimental settings. The stochastic independence of hidden and setting variables is called: freedom of choice, free will, measurement independence or no…
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements…
This is a brief review of the experimental and theoretical quantum computing. The hopes for eventually building a useful quantum computer rely entirely on the so-called "threshold theorem". In turn, this theorem is based on a number of…
We study random joint choice rules, allowing for interdependence of choice across agents. These capture random choice by multiple agents, or a single agent across goods or time periods. Our interest is in separable choice rules, where each…
It is a well-known fact in classical information theory that no deterministic procedure can extract close-to-ideal randomness from an arbitrary entropy source. On the other hand, if additional knowledge about the source is available --…
Consequences of the basic and most evident consistency requirement-that measured events cannot happen and not happen at the same time-are shortly reviewed. Particular emphasis is given to event forecast and event control. As a consequence,…
We describe how to device-independently generate a set of quantum states for which unambiguous state discrimination is not possible. First, we derive a formula that a certain non-signaling black box must satisfy. Then, we describe how to…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
We consider the problem of discriminating between states of a specified set with maximum confidence. For a set of linearly independent states unambiguous discrimination is possible if we allow for the possibility of an inconclusive result.…
We establish a generic result concerning order independence of a dominance relation on finite games. It allows us to draw conclusions about order independence of various dominance relations in a direct and simple way.
We model stochastic choices with categorization. The agent preliminarly groups alternatives in homogenous disjoint classes, then randomly chooses one class and randomly picks an item within the selected class. We give a formal definition of…
In this paper, we prove a conditional limit theorem for independent not necessarily identically distributed random variables. Namely, we obtain the asymptotic distribution of a large number of them given the sum.