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Compressive Direct Measurement of the Quantum Wave Function

Mirhosseini, Mohammad and Magaña-Loaiza, Omar S. and Hashemi Rafsanjani, Seyed Mohammad and Boyd, Robert W. (2014) Compressive Direct Measurement of the Quantum Wave Function. Physical Review Letters, 113 (9). Art. No. 090402. ISSN 0031-9007. doi:10.1103/physrevlett.113.090402.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Hashemi Rafsanjani, Seyed Mohammad0000-0001-7718-5654
Boyd, Robert W.0000-0002-1234-2265
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.
Funding AgencyGrant Number
Defense Threat Reduction Agency (DTRA)HDTRA1-10-1-0025
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Canada Research Chairs ProgramUNSPECIFIED
Consejo Nacional de Ciencia y Tecnología (CONACYT)UNSPECIFIED
Issue or Number:9
Classification Code:PACS numbers: 03.65.Ta, 03.65.Wj, 42.15.Dp, 42.50.Ex
Record Number:CaltechAUTHORS:20190628-110703950
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:96831
Deposited By: George Porter
Deposited On:01 Jul 2019 15:21
Last Modified:16 Nov 2021 17:24

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