A note on many valued quantum computational logics

TL;DR

This paper explores three-valued quantum computational logics within the Hilbert space C^3, extending quantum gates and characterizing states through effect probability, offering insights beyond the standard binary quantum computation framework.

Contribution

It introduces a three-valued quantum logic framework, extending gates and analyzing states using effect probability, which is a novel approach in quantum computation theory.

Findings

Extended quantum gates to three-valued logic

Characterized states using effect probability

Provided a framework for three-valued quantum computation

Abstract

The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space C^3, we discuss extensions of several gates to this space and, using the notion of effect probability, we provide a characterization of its states.