Extracting Classical Information from Quantum States: Fundamental Limits, Adaptive and Finite-Length Measurements

Motivated by the increasing demand for more powerful and efficient optical communication systems, quantum mechanics of information processing has become the key element in determining the fundamental limits of physical channels, and in designing quantum communication systems that approach those fundamental limits. To achieve higher data rate over quantum optical channels, we need to efficiently extract classical information from quantum states. However, peculiar properties of quantum states, such as the no-cloning theorem and the non-reversible measurement process, provide new challenges in the measurement of quantum states; in quantum information science, there is no concept analogous to sufficient statistics in classical information science. Therefore, to extract as much information as possible from quantum states, it is important to choose the right measurement process. In this talk, we investigate the fundamental question of how to design the measurement process to efficiently extract information from quantum states. The analysis and new insights into the measurement process of quantum states that we develop can be used to improve not only current quantum optical communication systems, but also classical information processing, where the data is too big to be handled with sufficient statistics. Our work would help develop new concepts of efficient statistics that provide systematic ways to choose useful information among big data while discarding the rest.