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An extended quantum process algebra (eQPAlg) approach for distributed quantum systems

Salman Haider, Syed Asad Raza Kazmi

TL;DR

This work has ameliorated the existing rules of Lalire's quantum process algebra QPAlg by introducing the concept of formally specifying the Quantum teleportation protocol and introducing the formal description of protocol by using programs that best explains its working and satisfies the specification.

Abstract

In this work, we have expounded the communication procedure of quantum systems by means of process algebra. The main objective of our research effort is to formally represent the communication between distributed quantum systems. In this new proposed communication model we have ameliorated the existing rules of Lalire's quantum process algebra QPAlg. We have brought some important modification in QPAlg by introducing the concept of formally specifying the Quantum teleportation protocol. We have further introduced the formal description of protocol by using programs that best explains its working and satisfies the specification. Examples have been provided to describe the working of the improved algebra that formally explain the sending and receiving of both classical as well as quantum data, keeping in mind the principal features of quantum mechanics.

An extended quantum process algebra (eQPAlg) approach for distributed quantum systems

TL;DR

This work has ameliorated the existing rules of Lalire's quantum process algebra QPAlg by introducing the concept of formally specifying the Quantum teleportation protocol and introducing the formal description of protocol by using programs that best explains its working and satisfies the specification.

Abstract

In this work, we have expounded the communication procedure of quantum systems by means of process algebra. The main objective of our research effort is to formally represent the communication between distributed quantum systems. In this new proposed communication model we have ameliorated the existing rules of Lalire's quantum process algebra QPAlg. We have brought some important modification in QPAlg by introducing the concept of formally specifying the Quantum teleportation protocol. We have further introduced the formal description of protocol by using programs that best explains its working and satisfies the specification. Examples have been provided to describe the working of the improved algebra that formally explain the sending and receiving of both classical as well as quantum data, keeping in mind the principal features of quantum mechanics.

Paper Structure

This paper contains 47 sections, 6 theorems, 73 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Quantum Computation & Communication
  3. Algebra of Quantum Processes
  4. Overview of this paper
  5. Preliminaries
  6. Linear Algebra: Vector Spaces and Operators
  7. Qubit
  8. Vector Spaces
  9. Basis and Dimension
  10. Inner Product
  11. Bra-ket Notation
  12. The Trace of an operator
  13. Hilbert Space
  14. Tensor Product
  15. Quantum Mechanics
  16. ...and 32 more sections

Key Result

Theorem 1

A specification is a statement written using mathematical expressions that is used to describe a system during the system analysis, system design and requirement analysis. A specification is generally not an executable program. A specification is said to be implementable if there is at least one out

Figures (4)

  • Figure 1: Informal description of Protocol
  • Figure 2: Behaviour of Alice
  • Figure 3: Behaviour of Bob
  • Figure 4: Behaviour of BuildEPR

Theorems & Definitions (6)

  • Theorem 1: Specification
  • Theorem 2: Program
  • Theorem 3
  • Theorem 4
  • Theorem 5
  • Theorem 6