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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Additional details
- Eprint ID
- 96831
- Resolver ID
- CaltechAUTHORS:20190628-110703950
- Defense Threat Reduction Agency (DTRA)
- HDTRA1-10-1-0025
- Defense Advanced Research Projects Agency (DARPA)
- Canada Research Chairs Program
- Consejo Nacional de Ciencia y Tecnología (CONACYT)
- NSF
- PHY-1203931
- Created
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2019-07-01Created from EPrint's datestamp field
- Updated
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2023-02-08Created from EPrint's last_modified field