Epistemic Quantum Computational Structures in a Hilbert-space Environment

Abstract

Quantum computation and quantum computational logics are intrinsically connected with some puzzling epistemic problems. In the framework of a quantum computational approach to epistemic logic we investigate the following question: is it possible to interpret the basic epistemic operations (having information, knowing) as special kinds of Hilbert-space operations? We show that non-trivial knowledge operations cannot be represented by unitary operators. We introduce the notions of strong epistemic quantum computational structure and of epistemic quantum computational structure, where knowledge operations are identified with special examples of quantum operations. This represents the basic tool for developing an epistemic quantum computational semantics, where epistemic sentences (like “Alice knows that the spin-value in the x-direction is up”) are interpreted as quantum pieces of information that may be stored by quantum objects.