21 May 2015 Complementary imaging with compressive sensing
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Abstract
Measurements on quantum systems are always constrained by uncertainty relations. For traditional, projective measurements, uncertainty relations correspond to resolution limitations; a detector's position resolution is increased at the cost of its momentum resolution and vice-versa. However, many experiments in quantum measurement are now exploring non- or partially-projective measurements. For these techniques, measurement disturbance need not manifest as a blurring in the complementary domain. Here, we describe a technique for complementary imaging | obtaining sharp position and momentum distributions of a transverse optical field with a single set of measurements. Our technique consists of random, partially-projective filtering in position followed by projective measurements in momentum. The partial-projections extract information about position at the cost of injecting a small amount of noise into the momentum distribution, which can still be directly imaged. The position distribution is recovered via compressive sensing.
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Gregory A. Howland, James Schneeloch, Daniel J. Lum, Samuel H. Knarr, John C. Howell, "Complementary imaging with compressive sensing", Proc. SPIE 9500, Quantum Information and Computation XIII, 95000D (21 May 2015); doi: 10.1117/12.2177002; https://doi.org/10.1117/12.2177002
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