Realization of a causal-modeled delayed-choice experiment using single photons

Shang Yu, Yong-Nan Sun, Wei Liu, Zhao-Di Liu, Zhi-Jin Ke, Yi-Tao Wang, Jian-Shun Tang, Chuan-Feng Li, and Guang-Can Guo

Phys. Rev. A 100, 012115 – Published 15 July 2019

Abstract

Wave-particle duality constitutes one of the most intriguing features in quantum physics. A well-known gedanken experiment that provides evidence for this is Wheeler's delayed-choice experiment based on a Mach-Zehnder interferometer [J. A. Wheeler, in Mathematical Foundations of Quantum Theory, edited by A. R. Marlow (Academic, New York, 1978), pp. 9–48; in Quantum Theory and Measurement, edited by J. A. Wheeler and W. H. Zurek (Princeton University Press, Princeton, 1984), pp. 182–213]. Many different versions of delayed-choice experiments have been conducted with both classical and quantum detecting devices. Recently, it was proposed that the delayed-choice experiment could be devised from the perspective of a device-independent prepare-and-measure scenario [R. Chaves et al., Causal Modeling the Delayed-Choice Experiment, Phys. Rev. Lett. 120, 190401 (2018)]. In our work, we experimentally realize this modified version with a deterministic single-photon source and examine the wave-particle objective in a causal-modeled scheme without the assistance of entanglement, which is achieved by violating the dimension-witness inequalities. Our experiment also provides an intriguing perspective and exhibits the benefits of studying quantum theory from the casual model point of view.

Received 13 June 2018
Revised 24 January 2019

DOI:https://doi.org/10.1103/PhysRevA.100.012115

Physics Subject Headings (PhySH)

Optical tests of quantum theory Quantum communication Quantum correlations in quantum information Quantum foundations Quantum information processing

Quantum Information, Science & TechnologyGeneral Physics

Authors & Affiliations

Shang Yu, Yong-Nan Sun, Wei Liu, Zhao-Di Liu, Zhi-Jin Ke, Yi-Tao Wang^*, Jian-Shun Tang^†, Chuan-Feng Li ^‡, and Guang-Can Guo

CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

^*yitao@ustc.edu.cn
^†tjs@ustc.edu.cn
^‡cfli@ustc.edu.cn

Compatibility of causal hidden-variable theories with a delayed-choice experiment

He-Liang Huang, Yi-Han Luo, B. Bai, Y.-H. Deng, H. Wang, Q. Zhao, H.-S. Zhong, Y.-Q. Nie, W.-H. Jiang, X.-L. Wang, Jun Zhang, Li Li, Nai-Le Liu, Tim Byrnes, J. P. Dowling, Chao-Yang Lu, and Jian-Wei Pan

Phys. Rev. A 100, 012114 (2019)

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Vol. 100, Iss. 1 — July 2019

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Figure 1
Causal model and PAM scenario for the delayed-choice experiment. (a) Directed acyclic graph representation of the causal structures for the delayed-choice experiment. Under the assumption of nonretrocausality (neglecting the gray dashed line), the variables $Y$ and $Λ$ should be statistically independent. When the retrocausality is allowed (including the gray dashed line), there will be causal influence between the variables $Y$ and $Λ$ . (b) Device-independent scenario for testing the delayed-choice experiment. When button $X$ is pressed, the state preparator emits a particle in a state $ρ (x)$ that will be sent to a measurement device. When button $Y$ is pressed, the device performs measurement on the particle and the measurement produces outcomes $D$ .
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Figure 2
Experimental setup. The single-photon source is generated from a hBN sample that is pumped by a 50- $μ W$ 532-nm laser. After the photon enters the interferometer (at BS1), a fixed phase $φ_{x_{i}}$ is applied on path $a$ by tilting the corresponding glass plate at the preparation stage. The photon is then delayed 300 ns by a 60-m-long fiber (the optical length before the fiber is unbalanced and the fiber can be split into the two isolated channels from both the polarization and coherence-time perspective). The attenuator in path $a$ is applied to adjust the transmittance. A QRNG-based switch (QRS) inside the interferometer enables the measurement bases to be chosen independently. Two phases on the measurement stage $σ_{y_{1}}$ and $σ_{y_{2}}$ are realized by glass plates similar to the $φ_{x_{i}}$ at the preparation stage and the photon then is detected after BS2. The HWPs are all rotated at $45^{\circ}$ if there are no special notes. Then the dimension-witness results can be calculated from the coincidence events from ports 1, 2, and $★$ for stage $Y_{1}$ or from ports 3, 4, and $★$ for stage $Y_{2}$ , respectively. The second-order correlation of the SPS can also be obtained by the total counts from the same data record (ports 1–4, without port $★$ ).
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Figure 3
Antibunching result of the SPS that is derived from the same data in experiment. The green dots are the normalized coincidence-counting results and the orange line is the theoretical fit for the data. The fitting function for the second-order time correlation is $g^{(2)} (t) = 1 - α e^{- | t | / τ}$ , where $t$ is the time delay and $α$ and $τ$ are the fitting parameters. The fitting results show the lifetime $τ = 3.193 \pm 0.136$ ns.
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Figure 4
Experimental results of the dimension-witness tests. (a) Experimental results of the dimension witness $| Det (W_{2}) |$ when the real transmittance coefficients $T_{a}$ of one path of the MZ interferometer is varied. (b) Results of the dimension witness $I_{DW}$ at the maximal violation setting. Theoretical and experimental values of $〈 D_{00} 〉$ , $〈 D_{01} 〉$ , $〈 D_{10} 〉$ , $〈 D_{11} 〉$ , and $〈 D_{20} 〉$ are illustrated, which are the terms in the dimension witness $I_{DW}$ with maximal violation. The error bars representing one standard deviation are obtained from 30 identical experimental procedures. (c) Experimental results of the dimension witness $I_{DW}$ with fixed phase $φ_{x_{i}}$ at the preparation stage and different measurement settings. The error range of the data is represented by the two gray edges. (d) Relationship between $φ_{x_{i}}$ and the retrocausality $R$ . The lines with different colors are the theoretical values when one of the phase shifts $φ_{x_{i}}$ is changed at the preparation. The orange circles, green squares, and purple triangles with error bars denote the corresponding experimental values.
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Figure 5
Antibunching result of the SPS measured with high precision. The green dots are the normalized coincidence-counting results and the orange line is the theoretical fitting for these data. The fitting function for the second-order time correlation is $g^{(2)} (t) = 1 - α e^{- | t | / τ}$ , where $t$ is the coincidence-counting delay and $α$ and $τ$ are the fitting parameters.
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