Quantum Direct Communication using Quantum Walks

Abstract

Quantum computation and quantum information have been one of the most extensive fields of research for the past three decades. Many groundbreaking quantum algorithms have been designed, which can perform the assigned tasks much faster than their classical counterparts. Shor's algorithm, one of the most well-known quantum algorithms, can be used to prime factorize large integers in polynomial time, while even the best classical integer factorization algorithms are exponential in time. As the security of most classical cryptosystems rely on the di culty to prime-factorize large numbers, the Shor's algorithm, if implemented on a scalable quantum computer, can compromise almost all of the classical cryptosystems that are widely used today. Hence, the requirement of quantum cryptography is greatly essential. In this thesis, I attempt to look into the possibility of exploiting quantum walks for the purposes of quantum cryptography. Quantum walks are the quantum analogues of the classical random walks. Unlike classical random walks, Quantum walks have unique properties such as superposition and entanglement of the position and the coin spaces, which can be exploited to design unconditionally secure quantum cryptographic protocols. I propose two new protocols, namely a Quantum Secure Direct Communication (QSDC) protocol and a Controlled Quantum Dialogue (CQD) protocol using discrete-time quantum walks on a cycle. The proposed protocols have been shown to be unconditionally secure against various attacks such as the intercept-resend attack, the denial of service attack, and the man-in-the-middle attack. Additionally, the proposed CQD protocol is shown to be unconditionally secure against an untrusted service provider. Also, it is shown that the proposed protocols are more secure against the intercept resend attack as compared to the qubit based LM05 protocol.