Chin. Phys. Lett.  2020, Vol. 37 Issue (8): 080301    DOI: 10.1088/0256-307X/37/8/080301
Direct Strong Measurement of a High-Dimensional Quantum State
Chen-Rui Zhang1,2, Meng-Jun Hu1,2*, Guo-Yong Xiang1,2*, Yong-Sheng Zhang1,2*, Chuan-Feng Li1,2, and Guang-Can Guo1,2
1CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
2CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China
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Chen-Rui Zhang, Meng-Jun Hu, Guo-Yong Xiang et al  2020 Chin. Phys. Lett. 37 080301
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Abstract It is of great importance to determine an unknown quantum state for fundamental studies of quantum mechanics, yet it is still difficult to characterize systems of large dimensions in practice. Although the scan-free direct measurement approach based on a weak measurement scheme was proposed to measure a high-dimensional photonic state, how weak the interaction should be to give a correct estimation remains unclear. Here we propose and experimentally demonstrate a technique that measures a high-dimensional quantum state with the combination of scan-free measurement and direct strong measurement. The procedure involves sequential strong measurement, in which case no approximation is made similarly to the conventional direct weak measurement. We use this method to measure a transverse state of a photon with effective dimensionality of $65000$ without the time-consumed scanning process. Furthermore, the high fidelity of the result and the simplicity of the experimental apparatus show that our approach can be readily used to measure the complex field of a beam in diverse applications such as wavefront sensing and quantitative phase imaging.
Received: 10 April 2020      Published: 28 July 2020
PACS:  03.67.-a (Quantum information)  
  42.50.-p (Quantum optics)  
  42.50.Tx (Optical angular momentum and its quantum aspects)  
Fund: Supported by the National Natural Science Foundation of China (Grant Nos. 11574291, 11774334, 11774335, 11674306 and 61590932), the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB01030200), the National Key Research and Development Program of China (Grant Nos. 2016YFA0301300, 2016YFA0301700 and 2017YFA0304100), the Key Research Program of Frontier Science, CAS (Grant No. QYZDY-SSW-SLH003), and Anhui Initiative in Quantum Information Technologies.
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Chen-Rui Zhang
Meng-Jun Hu
Guo-Yong Xiang
Yong-Sheng Zhang
Chuan-Feng Li
and Guang-Can Guo
[1] Dieks D 1982 Phys. Lett. A 92 271
[2] Wootters W K and Zurek W H 1982 Nature 299 802
[3] Cramer M, Plenio M B, Flammia S T, Somma R, Gross D, Bartlett S D, Landon-Cardinal O, Poulin D and Liu Y K 2010 Nat. Commun. 1 149
[4] James D F, Kwiat P G, Munro W J and White A G 2005 Asymptotic Theory of Quantum Statistical Inference: Selected Papers (Singapore: World Scientific) pp 509–538
[5]Paris M and Rehacek J 2004 Quantum State Estimation in Lecture Notes in Physics (Berlin: Springer)
[6] Resch K J, Walther P and Zeilinger A 2005 Phys. Rev. Lett. 94 070402
[7] Smithey D, Beck M, Raymer M G and Faridani A 1993 Phys. Rev. Lett. 70 1244
[8] Vogel K and Risken H 1989 Phys. Rev. A 40 2847
[9] Agnew M, Leach J, McLaren M, Roux F S and Boyd R W 2011 Phys. Rev. A 84 062101
[10] Schmied R 2016 J. Mod. Opt. 63 1744
[11] Lundeen J S, Sutherland B, Patel A, Stewart C and Bamber C 2011 Nature 474 188
[12] Mirhosseini M, Magaña-Loaiza O S, Rafsanjani S M H and Boyd R W 2014 Phys. Rev. Lett. 113 090402
[13] Shi Z, Mirhosseini M, Margiewicz J, Malik M, Rivera F, Zhu Z and Boyd R W 2015 Optica 2 388
[14] Lundeen J S and Bamber C 2012 Phys. Rev. Lett. 108 070402
[15] Salvail J Z, Agnew M, Johnson A S, Bolduc E, Leach J and Boyd R W 2013 Nat. Photon. 7 316
[16] Malik M, Mirhosseini M, Lavery M P, Leach J, Padgett M J and Boy R W 2014 Nat. Commun. 5 3115
[17] Aharonov Y, Albert D Z and Vaidman L 1988 Phys. Rev. Lett. 60 1351
[18] Dressel J, Malik M, Miatto F M, Jordan A N and Boyd R W 2014 Rev. Mod. Phys. 86 307
[19] Jozsa R 2007 Phys. Rev. A 76 044103
[20] Vallone G and Dequal D 2016 Phys. Rev. Lett. 116 040502
[21] Kedem Y and Vaidman L 2010 Phys. Rev. Lett. 105 230401
[22] Bolduc E, Bent N, Santamato E, Karimi E and Boyd R W 2013 Opt. Lett. 38 3546
[23] Fickler R, Lapkiewicz R, Plick W N, Krenn M, Schaeff C, Ramelow S and Zeilinger A 2012 Science 338 640
[24] Mirhosseini M, Malik M, Shi Z and Boyd R W 2013 Nat. Commun. 4 2781
[25] Molina-Terriza G, Torres J P and Torner L 2007 Nat. Phys. 3 305
[26] Bamber C, Sutherland B, Patel A, Stewart C and Lundeen J 2012 Opt. Express 20 2034
[27] Calderaro L, Foletto G, Dequal D, Villoresi P and Vallone G 2018 Phys. Rev. Lett. 121 230501
[28] Denkmayr T, Geppert H, Lemmel H, Waegell M, Dressel J, Hasegawa Y and Sponar S 2017 Phys. Rev. Lett. 118 010402
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