Quantum Measurement and Its Applications in Quantum Optical Systems

Abstract

Quantum measurement is the cornerstone of quantum computing and quantum information. It has many exciting applications. Various quantum optical systems are key to experimental physics because of their high precision and well controllability. In this dissertation, we focus on study of quantum measurement and its applications in quantum optical systems. We first study the fundamental trade-off relation between information gain and fidelity during successive weak QND measurement. Then we evaluate the effectiveness of quantum measurement reversal on quantum state protection under non-ideal detection efficiency. A linear optical setup is proposed for experimental verification of our result. Finally, we explore the performance of non-Gaussian two-mode entangled states for quantum illumination, which is an application of quantum state discrimination. For successive weak QND measurements, we show that the information gain increases monotonically with respect to the number of measurements. Meanwhile the fidelity shows oscillatory decreasing behavior, which results from interference terms between photon numbers. We conclude that a greater information gain does not always imply a worse fidelity. For non-ideal quantum measurement reversal, we derive how quantum states evolve in quantum reversal under finite effective monitoring efficiency. Fidelity and concurrence are then calculated to evaluate the effectiveness of state protection using reversal. Generally the performance is weakened by finite monitoring efficiency. The negative effect of measurement reversal can dominate under certain conditions. A criterion that decides whether to apply state protection using measurement reversal is given. As for quantum illumination, we conclude that non-Gaussian operations can enhance the performance, i.e., achieve lower error probability by introducing both stronger entanglement and larger average photon numbers. However, if the signal strength is a concern, two-mode squeezed states (TMSS) performs better than other non-Gaussian states under the same output signal strength. When applying a coherent superposition of photon subtraction and photon addition to enhance quantum illumination, we show that optimal error probability is achieved by an asymmetrical operation.