Theoretical Study Of Quantum Measurement And Control In Open Systems

Without measurement, it is impossible to know and understand this world. Up to now, world is controlled by quantum mechanics that is almost universally accepted. Therefore, quantum measurement is revested with profound and lasting meaning. On the one hand, quantum measurement theory provides the essential correlation between quantum form and familiar macroscopical device. On the other hand, application of quantum measurement to control system plays an im-portant role in the quantum information process or other fields. Due to that any real system must interact with surrounding environment, we have to consider the quantum measurement and control about open system.In this dissertation, we study the issue and focus on the application in quan-tum information science. It is divided into the following several aspects:1. Photons leak from a cavity can carry the information of a system in the optical cavity. One can perform a continuous measurement on the leaking photons to obtain a spectrum. We generalize the analytical method to reveal the dynamics of the system in spin environments and compare the strength of Markovian or non-Markovian effect. Besides, continuous measurement can help to justify whether there are correlations between two environments.2. Study the question about precision of frequency measurements in correlat-ed Markovian and non-Markovian environments. Using a variational approach, we obtain the precision bounds of frequency measurements. The metrological equivalence of product states and maximally entangled states persisting in max-imally correlated Markovian and non-Markovian environments is verified using a standard Ramsey spectroscopy setup. Furthermore, we find that optimal mea-surements can be used to achieve a much higher resolution than standard Ramsey spectroscopy in correlated environments.3. We explore the situation that the degree of fuzziness in the coarsened references of measurements can change with the rotation angle between two states (different rotation angles represent different references). The results show:for the fuzziness of Hamiltonian alone, the degree of fuzziness for reference will change with the rotation angle between two states, and the quantum effects can still be observed no matter how much the degree of fuzziness of Hamiltonian; for the fuzziness of timing, the degree of coarsening reference is unchanged with the rotation angle. During the rotation of the measurement axis, the decoherence environment can also help the classical-to-quantum transition due to changing the direction of measurement axis.4. Amir, et.al found that a signal can be encoded in the choice of the mea-surement basis of one of the communicating parties, while the outcomes of the measurement are irrelevant for the communication and therefore may be discard-ed. However, it was not secure for communication. We utilize the outcomes of measurement and separate the Hilbert space to propose a corresponding secure communication protocol. And error correction code is used to increase the fault tolerance of the signal transmission against noise.5. We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Marko-vian to a non-Markovian regime with the extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian-non-Markovian (both of two local dynamics are non-Markovian) or Markovian-non-Markovian, but not under the condition of Markovian-Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian-Markovian. It shows that the function of correlations between two environments has an up-per bound, which makes a flow of information from the environment back to the global system beginning finitely earlier than that back to one of the two local systems, not infinitely. Then, we proposed two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration we found that the self-correlation (internal correlation) of each environment promotes the nonlocal non-Markovian effects.