Nonlinear and Probabilistic Analysis with Frames
Abstract
This proposal seeks to advance our understanding of nonlinear and probabilistic analysis in the stochastic control settings found in quantum information applications, with eventual application in quantum computing. The approach here is a novel application of Frame theory (involving overdetermined/redundant vector bases in a Hilbert space) to three particular problems that arise in quantum information processing: 1) robust quantum state detection and estimation, 2) optimal quantum frames, and 3) redundant quantum representations and dimension reduction. Recent progress on fundamental topics of frame theory (e.g., the Kadison-Singer problem. the Paulson problem) show promise of advances by frame theory on these questions. Given a positive operator-valued measure, the quantum detection and estimation problem asks to robustly identify a quantum state from a set of quantum measurements. Probabilistic frames will be used to try to address this by recasting the issue as an optimization problem in quantum frames.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1610008
Entities
People
- Radu Bălan
Organizations
- Army Contracting Command
- United States Army
- University of Maryland