Resource theory of superposition: State transformations

Equal Superposition Transformations and Quantum Random Walks

The largest ensemble of qubits which satisfy the general transformation of equal superposition is obtained by different methods, namely, linearity, no-superluminal signalling and non-increase of entanglement under LOCC. We also consider the associated quantum random walk and show that all unitary balanced coins give the same asymmetric spatial probability distribution. It is further illustrated...

Superposition modulo theory

This thesis is about the Hierarchic Superposition calculus SUP(T) and its application to reasoning in hierarchic combinations FOL(T) of the free first-order logic FOL with a background theory T where the hierarchic calculus is refutationally complete or serves as a decision procedure. Particular hierarchic combinations covered in the thesis are the combinations of FOL and linear and non-linear ...

Superposition Modulo a Shostak Theory

A Study on Properties of Dempster-Shafer Theory to Probability Theory transformations

In this paper, five conditions that have been proposed by Cobb and Shenoy are studied for nine different mappings from the Dempster-Shafer theory to the probability theory. After comparing these mappings, one of the considerable results indicates that none of the mappings satisfies the condition of invariance with respect to the marginalization process. In more details, the main reason for this...

Superposition of Transcriptional Behaviors Determines Gene State

We introduce a novel technique to determine the expression state of a gene from quantitative information measuring its expression. Adopting a productive abstraction from current thinking in molecular biology, we consider two expression states for a gene--Up or Down. We determine this state by using a statistical model that assumes the data behaves as a combination of two biological distribution...