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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 rates 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 thesis, we investigate the fundamental question of how to design the measurement process to efficiently extract information from quantum states. First, we consider adaptive measurement, with which we measure each received quantum state one at a time, and then update the next measurement process based on the previous observations. We show that for binary hypothesis testing between two ideal laser light pulses, if we update the adaptive measurement to maximize the communication efficiency at each instant, based on recursively updated knowledge of the receiver, then we can achieve the theoretical lower bound of the detection error probability. Using this viewpoint, we give a natural generalization of the adaptive measurement to general M -ary hypothesis testing problems. We also analyze the information capacity with adaptive measurement, and compare the result with that for direct detection receivers and the ultimate capacity of quantum channels (the Holevo limit). We also investigate finite-blocklength joint receivers. The ultimate capacity of quantum channels is calculated under the assumption that an infinite number of quantum states can be collectively measured in one shot. However, this assumption becomes the primary barrier that prevents practical implementations of capacity-achieving joint de-