Based on the theory of quantum mechanics, intrinsic randomness in measurement distinguishes quantum effects from classical ones. From the perspective of states, this quantum feature can be summarized as coherence or superposition in a specific (classical) computational basis. Recently, by regarding coherence as a physical resource, Baumgratz et al. present a comprehensive framework for coherence measures. Here, we propose a quantum coherence measure essentially using the intrinsic randomness of measurement. The proposed coherence measure provides an answer to the open question in completing the resource theory of coherence. Meanwhile, we show that the coherence distillation process can be treated as quantum extraction, which can be regarded as an equivalent process of classical random number extraction. From this viewpoint, the proposed coherence measure also clarifies the operational aspect of quantum coherence. Finally, our results indicate a strong similarity between two types of quantumness -coherence and entanglement.

Quantum physics can be exploited to generate true random numbers, which have important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumnesscoherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. On the basis of the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modelling the devices. The second category is self-testing QRNG, in which verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category that provides a tradeoff between the trustworthiness on the device and the random number generation speed.

Relation classification is a crucial ingredient in numerous information extraction systems seeking to mine structured facts from text. We propose a novel convolutional neural network architecture for this task, relying on two levels of attention in order to better discern patterns in heterogeneous contexts. This architecture enables endto-end learning from task-specific labeled data, forgoing the need for external knowledge such as explicit dependency structures. Experiments show that our model outperforms previous state-of-the-art methods, including those relying on much richer forms of prior knowledge.

We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence measure over product bases. Any coherence measure of pure states, with extension to mixed states by convex roof, is the maximum entanglement generated by incoherent operations acting on the system and an incoherent ancilla. Remarkably, the generalized CNOT gate is the universal optimal incoherent operation. In this way, all convex-roof coherence measures, including the coherence of formation, are endowed with (additional) operational interpretations. By virtue of this connection, many results on entanglement can be translated to the coherence setting, and vice versa. As applications, we provide tight observable lower bounds for generalized entanglement concurrence and coherence concurrence, which enable experimentalists to quantify entanglement and coherence of the maximal dimension in real experiments.

We study random number generation using a biased source motivated by previous works on this topic, mainly, von Neumman (1951), Elias (1972), Knuth and Yao (1976) and Peres (1992). We study the problem in two cases: first, when the source distribution is unknown, and second, when the source distribution is known. In the first case, we characterize the functions that use a discrete random source of unknown distribution to simulate a target discrete random variable with a given rational distribution. We identify the functions that minimize the ratio of source inputs to target outputs. We show that these optimal functions are efficiently computable. In the second case, we prove that it is impossible to construct an optimal tree algorithm recursively, using algebraic decision procedures. Our model of computation is sufficiently general to encompass previously known algorithms for this problem. RANDOM NUMBER GENERATION USING A BIASED SOURCE BY SUNG-IL PAE ABSTRACT We study random number generation using a biased source motivated by previous works on this topic, mainly, von Neumman (1951), Elias (1972), Knuth and Yao (1976) and Peres (1992). We study the problem in two cases: first, when the source distribution is unknown, and second, when the source distribution is known. In the first case, we characterize the functions that use a discrete random source of unknown distribution to simulate a target discrete random variable with a given rational distribution. We identify the functions that minimize the ratio of source inputs to target outputs. We show that these optimal functions are efficiently computable. In the second case, we prove that it is impossible to construct an optimal tree algorithm recursively, using algebraic decision procedures. Our model of computation is sufficiently general to encompass previously known algorithms for this problem. iii ACKNOWLEDGMENTS I am deeply grateful to my advisor Michael C. Loui. He provided me with advice on almost every aspect of my life as a graduate student, not to mention the countless meetings and comments on my thesis work. I began working with him at an especially difficult time of my graduate study. Without his encouragements and guidance, the complexity of my life would have been even greater.