Quantum Bisimilarity is a Congruence under Physically Admissible Schedulers

TL;DR

This paper introduces a new quantum bisimilarity concept that is a congruence under physically admissible schedulers, aiding the modeling and verification of quantum concurrent systems.

Contribution

It proposes a quantum bisimilarity that is a congruence under physically admissible schedulers, addressing a key challenge in quantum process verification.

Findings

Bisimilarity is a congruence under physically admissible schedulers.

The approach effectively models quantum concurrent systems.

It resolves issues of spurious discrimination in quantum process equivalence.

Abstract

The development of quantum algorithms and protocols calls for adequate modelling and verification techniques, which requires abstracting and focusing on the basic features of quantum concurrent systems, like CCS and CSP have done for their classical counterparts. So far, an equivalence relation is still missing that is a congruence for parallel composition and adheres to the limited discriminating power implied by quantum theory. In fact, defining an adequate bisimilarity for quantum-capable, concurrent systems proved a difficult task, because unconstrained non-determinism allows to spuriously discriminate indistinguishable quantum systems. We investigate this problem by enriching a linear quantum extension of CCS with simple physically admissible schedulers. We show that our approach suffices for deriving a well-behaved bisimilarity that satisfies the aforementioned desiderata.