Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus

TL;DR

This paper demonstrates how the ZX-calculus, a diagrammatic language for quantum protocols, can be used to represent and analyze superdense coding with GHZ states and quantum key distribution with W-states, enhancing understanding and verification.

Contribution

It introduces the application of the ZX-calculus to superdense coding with GHZ states and quantum key distribution with W-states, extending categorical quantum mechanics to quantum security protocols.

Findings

ZX-calculus provides intuitive representations of superdense coding and QKD protocols.

The paper successfully models GHZ-based superdense coding in the ZX-calculus.

W-state QKD protocols are represented diagrammatically, facilitating analysis.

Abstract

Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify. This is why Coecke and Duncan have introduced a diagrammatic language for quantum protocols, called the ZX-calculus. This diagrammatic notation is both intuitive and formally rigorous. It is a simple, graphical, high level language that emphasises the composition of systems and naturally captures the essentials of quantum mechanics. In the author's MSc thesis it has been shown for over 25 quantum protocols that the ZX-calculus provides a relatively easy and more intuitive presentation. Moreover, the author embarked on the task to apply categorical quantum mechanics on quantum security; earlier works did not touch anything but Bennett and Brassard's quantum key distribution protocol, BB84. Superdense coding with the Greenberger-Horne-Zeilinger state and quantum key distribution with the W-state are presented in the ZX-calculus in this paper.