Compressively Characterizing High-Dimensional Entangled States with Complementary, Random Filtering
Abstract
The resources needed to conventionally characterize a quantum system are overwhelmingly large for high-dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general quantum states, strong projective measurement, and assumption free characterization. Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements. We recover sharp distributions with local, random filtering of the same ensemble in momentum followed by positionsomething the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5000 measurements to characterize a 65,536-dimensional state. Finally, we use entropic inequalities to witness entanglement without a density matrix. Our method represents the sea change unfolding in quantum measurement, where methods influenced by the information theory and signal-processing communities replace unscalable, brute-force techniquesa progression previously followed by classical sensing.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 30, 2016
- Accession Number
- AD1010504
Entities
People
- Daniel J. Lum
- Gregory A. Howland
- James Schneeloch
- John C. Howell
- Samuel H. Knarr
Organizations
- University of Rochester