Date of Degree
Janos A. Bergou
cloning; discrimination; implementation; quantum; realization; separation
This thesis reflects works previously published by the author and materials hitherto unpublished on the subject of quantum information theory. Particularly, results in optimal discrimination, cloning, and separation of quantum states, and their relationships, are discussed.
Our interest lies in the scenario where we are given one of two quantum states prepared with a known a-priori probability. We are given full information about the states and are assigned the task of performing an optimal measurement on the incoming state. Given that none of these tasks is in general possible to perform perfectly we must choose a figure of merit to optimize, and as we shall see there is always a trade-off between competing figures of merit, such as the likelihood of getting the desired result versus the quality of the result.
For state discrimination the competing figures of merit are the success rate of the measurement, the errors involved, and the inconclusiveness. Similarly increasing the separation between states comes at a cost of less frequent successful applications of the separation protocol. For cloning, aside from successfully producing clones we are also interested in the fidelity of the clones compared to the original state, which is a measure of the quality of the clones. Because all quantum operations obey the same set of conditions for evolution one may expect similar restrictions on disparate measurement strategies, and our work shows a deep connection between all three branches, with cloning and separation asymptotically converging to state discrimination.
Via Neumark's theorem, our description of these unitary processes can be implemented using single-photon interferometry with linear optical devices. Amazingly any quantum mechanical evolution may be decomposed as an experiment involving only lasers, beamsplitters, phase-shifters and mirrors. Such readily available tools allow for verification of the aforementioned protocols and we build upon existing results to derive explicit setups that the experimentalist may build.
Yerokhin, Vadim, "Optimal Measurements Tasks and Their Physical Realizations" (2015). CUNY Academic Works.