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 19200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.
| Original language | English (US) |
|---|---|
| Article number | 090402 |
| Journal | Physical Review Letters |
| Volume | 113 |
| Issue number | 9 |
| DOIs | |
| State | Published - Aug 27 2014 |
| Externally published | Yes |
Fingerprint
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Compressive direct measurement of the quantum wave function. / Mirhosseini, Mohammad; Magaña-Loaiza, Omar S.; Hashemi Rafsanjani, Seyed Mohammad; Boyd, Robert W.
In: Physical Review Letters, Vol. 113, No. 9, 090402, 27.08.2014.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Compressive direct measurement of the quantum wave function
AU - Mirhosseini, Mohammad
AU - Magaña-Loaiza, Omar S.
AU - Hashemi Rafsanjani, Seyed Mohammad
AU - Boyd, Robert W.
PY - 2014/8/27
Y1 - 2014/8/27
N2 - 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 19200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.
AB - 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 19200-dimensional state, a task that would require an unfeasibly large acquiring time with the standard direct measurement technique.
UR - http://www.scopus.com/inward/record.url?scp=84907360492&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84907360492&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.113.090402
DO - 10.1103/PhysRevLett.113.090402
M3 - Article
VL - 113
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 9
M1 - 090402
ER -