Interplay between Quantumness, Randomness, and Selftesting

Abstract

Quantum information processing shows advantages in many tasks, including quantum communication and computation, comparing to its classical counterpart. The essence of quantum processing lies on the fundamental difference between classical and quantum states. For a physical system, the coherent superposition on a computational basis is different from the statistical mixture of states in the same basis. Such coherent superposition endows the possibility of generating true random numbers, realizing parallel computing, and other classically impossible tasks such as quantum Bernoulli factory. Considering a system that consists of multiple parts, the coherent superposition that exists nonlocally on different systems is called entanglement. By properly manipulating entanglement, it is possible to realize computation and simulation tasks that are intractable with classical means. Investigating quantumness, coherent superposition, and entanglement can shed light on the original of quantum advantages and lead to the design of new quantum protocols. This thesis mainly focuses on the interplay between quantumness and two information tasks, randomness generation and selftesting quantum information processing. We discuss how quantumness can be used to generate randomness and show that randomness can in turn be used to quantify quantumness. In addition, we introduce the Bernoulli factory problem and present the quantum advantage with only coherence in both theory and experiment. Furthermore, we show a method to witness entanglement that is independent of the realization of the measurement. We also investigate randomness requirements in selftesting tasks and propose a random number generation scheme that is independent of the randomness source.