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Published August 29, 2014 | Published + Accepted Version
Journal Article Open

Compressive Direct Measurement of the Quantum Wave Function

Abstract

The direct measurement of a complex wave function has been recently realized by using weak values. In this Letter, we introduce a method that exploits sparsity for the compressive measurement of the transverse spatial wave function of photons. The procedure involves weak measurements of random projection operators in the spatial domain followed by postselection in the momentum basis. Using this method, we experimentally measure a 192-dimensional state with a fidelity of 90% using only 25 percent of the total required measurements. Furthermore, we demonstrate the measurement of a 19 200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.

Additional Information

© 2014 American Physical Society. (Received 13 May 2014; published 27 August 2014) We acknowledge helpful discussions with J. H. Eberly, B. Rodenburg, and Z. Shi. This work was supported by the DARPA/DSO InPho program, the U.S. Defense Threat Reduction Agency (Grant No. HDTRA1-10-1-0025), and the Canadian Excellence Research Chair (CERC) program. O. S. M.-L. also acknowledges support from the CONACyT. S. M. H. R. acknowledges financial support from NSF Grant No. PHY-1203931.

Attached Files

Published - PhysRevLett.113.090402

Accepted Version - 1404.2680.pdf

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August 20, 2023
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