Design, analysis and implementation of advanced quantum communication protocols
In this thesis we focus on designing protocols for quantum information processing tasks that can be implemented with current photonic technologies. We start by providing the first example of a communication model and a distributed task for which there exists a realistic quantum protocol asymptotically more efficient than any classical protocol, both in terms of communication and information resources. To this end, we extend the recently proposed coherent state mapping for quantum communication protocols, study the use of coherent state fingerprints over multiple channels and show their role in the design of an efficient quantum protocol for estimating the Euclidean distance between two real vectors within a constant factor. In the second part of the thesis, we propose a new problem in one-way communication model, Sampling Matching problem, for which there exists an exponential gap between a realistic quantum protocol and any randomized classical protocol within bounded error. We implement this problem using attenuated coherent states and linear optics, and show an advantage in using quantum resources from very low input sizes to the problem. This new proposal is a far simplified alternative to the previous problems in one-way communication model due to it requiring O(1) linear optical elements for implementation. This facilitates the implementation of the quantum protocol for arbitrarily large input sizes. Then we introduce a private-key quantum money-scheme with the verification protocol based on the Sampling Matching scheme. We look at the scheme when the Bank prepares notes as single photon superposition states. The features of our scheme include single-round classical interaction with the Bank, linear note re-usability, robustness against experimental imperfection, and an unconditional security against an adversary trying to forge the Bank note. We then follow up this work by proposing a practical quantum money-scheme when the Bank prepares notes as attenuated coherent states. This is an experimentally motivated framework which utilises the advantage offered by the Sampling Matching verification protocol that it requires only O(1) linear optical elements for implementation. Finally we introduce a programmable device whose input states control the the measure- ment operation. In particular, our device is the generalised Sylvester-Hadamard operation to discriminate two unknown coherent states in the setting of a single copy of one state (test state), and M −1 copies of the other state (reference state). Our distinguishing scheme involves M linear optics components (50/50 beam splitters), and M −1 single photon thresh- old detectors. We show that our setting strictly improves the soundness in discriminating two coherent states compared to the setting when one is provided only a single copy of the two states.