How is compressive sensing changing the world ? Here is one way: it makes quantum mechanics simpler to understand: Compressively characterizing high-dimensional entangled states with complementary, random filtering by Gregory A. Howland, Samuel H. Knarr, James Schneeloch, Daniel J. Lum, John C. Howell
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 position---something the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5,000 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 techniques---a progression previously followed by classical sensing.
- Simultaneous Measurement of Complementary Observables with Compressive Sensing
- Entropic Uncertainty Relations in Quantum Physics / On asymptotic structure in compressed sensing
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