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.

Date Published: 21 May 2015
PDF: 7 pages
Proc. SPIE 9500, Quantum Information and Computation XIII, 95000D (21 May 2015); doi: 10.1117/12.2177002

Published in SPIE Proceedings Vol. 9500:
Quantum Information and Computation XIII
Eric Donkor; Andrew R. Pirich; Michael Hayduk, Editor(s)