Quantum Search and Entanglement Sharing for Applications in Quantum Information Science
Date Issued
2009
Date
2009
Author(s)
Ju, Yi-Lin
Abstract
Quantum information science is a fascinating field of research that studies how to process information based on quantum mechanisms. Due to its interdisciplinary nature, potential applications can be found almost in every field of computer science and electrical engineering. This thesis aims to discuss how to apply quantum mechanics to different applications in quantum computing and quantum cryptography, including quantum search and entanglement distribution. irst, based on Grover''s quantum search algorithm, we give the quantum circuits for two applications, searching a phone book and breaking a symmetric cryptosystem. Although these two applications have quite different types of search criteria, they are both one-way functions and the proposed circuits can actually be generalized to any such problems. In this perspective, we propose a template of quantum circuits that is capable of searching the solution of a certain class of one-way functions.econd, we propose a protocol to securely distribute entanglement states and show how to use it to perform encrypted communication and broadcasting. In these applications, only legitimate users can decrypt the messages, whereas eavesdroppers, if existing, will receive garbage. In comparison with classical cryptographic protocols, the security of our protocols is guaranteed by the Heisenberg uncertainty principle of quantum mechanics, instead of unproven mathematical hard problems. hird, since the quantum channel needed in our entanglement sharing protocol might not be available under some circumstances, we study a quantum phenomenon called entanglement swapping, which can be used to distribute entanglement states without transmitting qubits. We propose two systematic methodologies so application-specific entanglement statesmong participants can be generated and distributed directly. The first method is based on Hadamard matrix, and can be used to perform authenticated encryption. The other one is based on quantum Fourier transform, and can be applied on multi-particle multi-level quantum systems. We describe its circuit design and demonstrate that it can be applied to distributed applications such as secret sharing. In comparison with classical cryptographic protocols, its security is guaranteed by quantum physics, instead of any unproven mathematic conjecture.
Subjects
quantum information science
quantum search
quantum entanglement
Type
thesis
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