Security Proof of the BB84 protocol and Device Independent Randomness Certification

Mishra, Abhishek (2022) Security Proof of the BB84 protocol and Device Independent Randomness Certification. Masters thesis, Indian Instritute of Science Education and Research Kolkata.

Text (MS dissertation of Abhishek Mishra (17MS100)) 17MS100_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Information theory was developed by Shannon as a mathematical theory to model tasks such as coding, communication and encryption. Quantum mechanics with its strange properties brings in more power over classical information processing. A lot of development has taken place at least theoretically that overpowers its classical counterpart such as faster search algorithms and prime factorization. Although these are lot faster than classical algorithms, the practical realizations have been hindered by decoherence in quantum computers. But, one information processing process i.e quantum key distribution has seen lot of progress after the BB84 QKD protocol for the simple reason that it can be done with existing technologies such as optical fibre. Plans for implementing QKD have also started in many places. Now, BB84 protocol promises unconditional security just based on principles of quantum mechanics. Such a giant promise has to be proved. In this thesis, we have explored this proof in quite a detail elaborating on the prerequisites like Quantum Error Correction, Quantum Cryptography and Entanglement distillation. The procedure of Entanglement distillation through error codes has been analysed rigorously. Also, in the concluding chapter, we have shown another groundbreaking use of Bell theorem. Its ability to certify randomness without any assumption of the devices used. Now, Bell value usually certifies non-locality but, with clever definition of randomness and device-Independence.

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