Holistic logical arguments in quantum computation

TL;DR

This paper explores a holistic approach to quantum computational logic, emphasizing global semantics and entanglement phenomena, contrasting with traditional compositional semantics in quantum computation.

Contribution

It introduces a holistic quantum logic framework where meanings are global objects, providing new insights into quantum semantics and logical arguments in quantum computation.

Findings

Holistic semantics captures entanglement effects.

Logical arguments reflect informal reasoning.

Global meanings differ from standard compositional approaches.

Abstract

Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way. The characteristic holistic features of the quantum theoretic formalism (which play an essential role in entanglement-phenomena) can be used in order to develop a holistic version of the quantum computational semantics. In contrast with the compositional character of most standard semantic approaches, meanings of formulas are here dealt with as global abstract objects that determine the contextual meanings of the formulas' components (from the whole to the parts). We present a survey of the most significant logical arguments that are valid or that are possibly violated in the framework of this semantics. Some logical features that may appear prima facie strange seem to reflect pretty well informal arguments that are currently used in our rational activity.