Michael D. Westmoreland

Reversibility of Local Transformations of Multiparticle Entanglement

We consider the transformation of multisystem entangled states by local quantum operations and classical communication. We show that, for any reversible transformation, the relative entropy of entanglement for any two parties must remain constant. This shows, for example, that it is not possible to convert 2N three-party GHZ states into 3N singlets, even in an asymptotic sense. Thus there is true three-party non-locality (i.e. not all three party entanglement is equivalent to two-party entanglement). Our results also allow us to make quantitative. statements about concentrating multi-particle entanglement. Finally, we show that there is true n-party entanglement for any n.

Capacities of Quantum Channels and Quantum Coherent Information

We derive relation between a quantum channels capacity to convey classical information and its ability to convey quantum information. We also show that these properties of a quantum channel are related to the channels ability to convey quantum coherent information.

Analysis of billiard ball computation using phase space logics

Abstract When analyzing individual gates in circuitry, one usually assumes that inputs are either 0 or 1, as are the outputs, but the fact is that these input values are really either “high” voltage or “low” voltage. Determining whether or not a given input is to be considered as high or low depends on a physical measurement of the voltage. Since physical measurement is never exact, it is more realistic to consider “high,” “low,” and “indeterminate,” hence considering three possible values, rather than two, when reasoning about computer hardware. When considering physical measurement as part of the determination as to what inputs and outputs are for a given gate, one can no longer reason about these gates using boolean logic. There are several possible non-boolean alternatives one may consider. We will examine motivation for some such alternatives and point out how we might apply them to a particular model of computation: the billiard ball model.

Derivation schemes in twin open set logic

Several logic-like structures have been developed to analyze classical mechanical systems. These phase space logics are examples of a wider class of structures known as derived logics. Many of the derived logics for classical systems are non-Boolean so it is natural to ask about the existence of derivation schemes in these logics. The prime example of a derivation scheme is the one in classical logic given by entailment, implication, and modus ponens. This chapter presents the relation between these three aspects of classical logic and shows that these three exist only when the logic is Boolean. The chapter then considers some possible alternative derivation schemes for the particular derived logic known as twin open set logic. We show how twin open set logic describes a collision model of computation. We then consider this collision model to choose between alternatives for a derivation scheme for twin open set logic when that logic is applied to collision models.

Zeno's arrow and classical phase space logics

We analyze the Zenos familiar paradox of the arrow using recently developed non-Boolean derived logics for classical systems. We show that the paradox depends upon a premise that is identically false in such logics, so that the language of experimental propositions is immune to the paradox.