Observational Equivalence Using Schedulers for Quantum Processes

TL;DR

This paper introduces a new observational equivalence for quantum processes in qCCS, utilizing schedulers to resolve nondeterminism and better capture process similarities.

Contribution

It proposes a novel notion of observational equivalence for quantum processes and explores how schedulers influence this equivalence in quantum process algebras.

Findings

Schedulers resolve nondeterminism in quantum processes.

Different scheduler restrictions affect observational equivalence.

The paper establishes relationships between schedulers and process equivalence.

Abstract

In the study of quantum process algebras, researchers have introduced different notions of equivalence between quantum processes like bisimulation or barbed congruence. However, there are intuitively equivalent quantum processes that these notions do not regard as equivalent. In this paper, we introduce a notion of equivalence named observational equivalence into qCCS. Since quantum processes have both probabilistic and nondeterministic transitions, we introduce schedulers that solve nondeterministic choices and obtain probability distribution of quantum processes. By definition, the restrictions of schedulers change observational equivalence. We propose some definitions of schedulers, and investigate the relation between the restrictions of schedulers and observational equivalence.