Quantum Control and Quantum Metrology: Applications of Quantum Entanglements
Abstract
Controlling the behavior of quantum systems lies at the heart of quantum information processing. All control protocols involve probing a primary quantum system, processing the acquired data to learn about the system s behavior, and using the processed data to change the behavior of the probing systems or the primary system. This proposal outlines research on four projects, all of which provide insight into how to sense and/or control quantum systems. Some of the projects are focused on developing efficient and accurate descriptions of the behavior of complex quantum systems; others are aimed directly at understanding quantum sensing and control. The four research projects are the following: Dynamics of Bose-Einstein condensates beyond mean eld. The spatio-temporal dynamics of dilute-gas Bose-Einstein condensates (BECs) are generally well described by the mean- eld Gross-Pitaevskii equation. This description fails, however, when particle correlations become important as, for example, when a BEC splits into spatial components as a potential barrier is raised within it. This project will develop a tractable formalism for analyzing such situations, based on the pair-correlated states introduced recently by UNM student Zhang Jiang and PI Caves. This formalism will provide an essential tool, well short of exact numerical integration of the many-body equations, for precision control of the behavior of BECs. Quantum-coherent ltering and quantum limits on waveform estimation. Treatments of quan- tum limits on parameter estimation typically assume the parameter to be estimated is static, but the relevant situation in an interferometric gravitational-wave detector or in microscopic opto-mechanical systems is that of sensing the time-dependent waveform of a force acting on a linear mechanical system. This project will catalogue the frequency-dependent spectra of standard quantum limits (SQLs) for such waveform estimation and of the corresponding fun- damental limits and will characterize and evaluate techniques of quantum-coherent ltering for beating the SQL. Quantum-circuit-based formulation of quantum control and feedback. Quantum-circuit dia- grams provide an ideal tool for classifying and understanding protocols for control and feed- back; their key advantage is that they separate cleanly the temporal and spatial features of a control protocol, making it easy to visualize the exchange of information, both quantum and classical, between quantum systems and the ow of such information in time. This research project aims to develop quantum-circuit diagrams as useful design tools and to understand whether and when coherent control protocols offer advantages over measurement-based con- trol and feedback. An ambitious part of this project is to begin to understand the difference between classical and quantum systems as the agents in control protocols. The origins of indeterminism and the emergence of quantum mechanics. There are only two really important questions for work on the foundations of quantum mechanics: Why indeter- minism? Why the superposition principle? This project aims to address these questions by making the noncontextuality of probability distributions the cornerstone that underlies quan- tum mechanics. It is easy to formulate toy theories of noncontexual probabilities that force one to indeterminism; indeed, such is the general situation. This project will seek additional prin- ciples that pick out uniquely the familiar quantum formalism of complex vector spaces. Along the way, this approach will give rise to theories alternative to quantum mechanics, to which the standard quantum formalism can be compared, for example, in information-processing power.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2016
- Source ID
- N000141512167
Entities
People
- Carlton M. Caves
Organizations
- Office of Naval Research
- United States Navy
- University of New Mexico