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arXiv:1404.0665

Security Analyses of Quantum Communication Protocols

Yong Wang

Published Mar 17, 2014• 1 citation
arXivHTMLPDF

Abstract

Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP,$π_{tc}$ to $π$ calculus, APPTC to probabilistic process algebra.In this book, we utilize truly concurrent process algebras APTC and APPTC to model quantum computing and unify quantum and classical computing.

DOI
10.48550/arxiv.1404.0665

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Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP,πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra.In this book, we utilize truly concurrent process algebras APTC and APPTC to model quantum computing and unify quantum and classical computing.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra. Now, it is the time to utilize truly concurrent process algebras APTC and APPTC to model quantum computing and unify quantum and classical computing. In this book, we introduce the preliminaries, the utilization of APTC to unify quantum and classical computing and its usage in verification of quantum communication protocols, the utilization of APPTC to unifying quantum and classical computing and its usage in verification of quantum communication protocols.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus , APPTC to probabilistic process algebra. And we also did some work on reversible process algebra and probabilistic truly concurrent process algebra. In this book, we utilize reversible truly concurrent process algebras APRTC and APPTC to model quantum computing and unify quantum and classical computing.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra, APTC with localities to process algebra with localities. In quantum process algebras, there are several well-known work, and we ever did some work to unify quantum and classical computing under the framework of ACP \cite{ACP} and probabilistic process algebra. Now, it is the time to utilize truly concurrent process algebras with localities to model quantum computing and unify quantum and classical computing in this book. Since this work is with localities, it is suitable to verify the distribution of quantum communication protocols.
Truly concurrent process algebras are generalizations to the traditional process algebras for true concurrency, CTC to CCS, APTC to ACP, πtcπ_{tc}πtc​ to πππ calculus, APPTC to probabilistic process algebra. And we also did some work on reversible process algebra and probabilistic truly concurrent process algebra. In this book, we utilize reversible truly concurrent process algebras APRTC and probabilistic process algebra APPTC to model quantum computing and unify quantum and classical computing.
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and distributed quantum computations, as well as quantum communication protocols, quantum to quantum communications which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts.Based upon an operational semantics which makes sure that quantum objects, operations and communications operate according to the postulates of quantum mechanics, a probabilistic branching bisimulation is defined among processes considered as having the same behavior.
Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate. Moreover, to model concurrent and distributed quantum computations, as well as quantum communication protocols, quantum to quantum communications which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined, named QPAlg for Quantum Process Algebra, which provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts. On the quantum side, QPAlg provides quantum variables, operations on quantum variables (unitary operators and measurement observables), as well as new forms of communications involving the quantum world. The operational semantics makes sure that these quantum objects, operations and communications operate according to the postulates of quantum mechanics.