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1

Jacques, V., E. Wu, F. Grosshans, F. Treussart, P. Grangier, A. Aspect, and J. F. Roch. "Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment." Science 315, no. 5814 (February 16, 2007): 966–68. http://dx.doi.org/10.1126/science.1136303.

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2

Tang, Jian-Shun, Yu-Long Li, Xiao-Ye Xu, Guo-Yong Xiang, Chuan-Feng Li, and Guang-Can Guo. "Realization of quantum Wheeler's delayed-choice experiment." Nature Photonics 6, no. 9 (August 19, 2012): 600–604. http://dx.doi.org/10.1038/nphoton.2012.179.

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3

Ardehali, M. "Quantum cryptography based on wheeler's delayed choice experiment." Physics Letters A 217, no. 6 (July 1996): 301–4. http://dx.doi.org/10.1016/0375-9601(96)00368-4.

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4

Jacques, V., E. Wu, F. Grosshans, F. Treussart, A. Aspect, Ph Grangier, and J. F. Roch. "Wheeler's delayed-choice thought experiment: Experimental realization and theoretical analysis." Annales de Physique 32, no. 2-3 (2007): 195–97. http://dx.doi.org/10.1051/anphys:2008041.

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5

Manning, A. G., R. I. Khakimov, R. G. Dall, and A. G. Truscott. "Wheeler's delayed-choice gedanken experiment with a single atom." Nature Physics 11, no. 7 (May 25, 2015): 539–42. http://dx.doi.org/10.1038/nphys3343.

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6

Zhao, S., S. Yuan, H. De Raedt, and K. Michielsen. "Computer simulation of Wheeler's delayed-choice experiment with photons." EPL (Europhysics Letters) 82, no. 4 (May 2008): 40004. http://dx.doi.org/10.1209/0295-5075/82/40004.

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7

Rössler, O. E. "Delayed Choice with Correlated Photons." Zeitschrift für Naturforschung A 43, no. 2 (February 1, 1988): 110–14. http://dx.doi.org/10.1515/zna-1988-0203.

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Abstract A new experiment in the foundations of quantum mechanics is proposed. The existence of correlated photons -first seen by Wheeler -can be taken as a hint to devise a ‘‘double-wing’’ delayed choice experiment in Wheeler’s sense. A path choice (polarization choice) measurement made on the one side should then block an interference type measurement made on the other side (‘‘distant choice’’). A precondition for the combined measurement to work in theory is that the correlated photons used are of the ‘‘prepolarized’’ (Selleri) rather than the ‘‘unpolarized’’ (Böhm) type. A first EPR experiment involving prepolarized photons was recently performed by Alley and Shih. It may be used as a partial experiment within the proposed experiment.
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8

Ye, Gen-Sheng, Biao Xu, Feng-Yuan Kuang, Hao-Xiang Liu, Shuai Shi, Yiqiu Ma, and Lin Li. "Wheeler’s delayed-choice experiment based on Rydberg atoms." Journal of Physics B: Atomic, Molecular and Optical Physics 55, no. 4 (February 16, 2022): 044002. http://dx.doi.org/10.1088/1361-6455/ac505e.

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Abstract The delayed choice gedanken-experiment initially proposed by J A Wheeler reveals the nontrivial features of wave–particle duality in quantum world, that is, the choice of whether to observe the particle/wave character of a quantum system at a delayed time can affect its evolution history. In this work, the Wheeler’s delayed-choice experiment is conducted and tested in a new regime based on a Rydberg-ground level atomic Mach–Zehnder interferometer with optical coherent manipulation. Our quantum system exhibits an excellent single-excitation of the collective atomic state due to the Rydberg blockade effect, and the delayed choice of the interferometer configuration is realized by a quantum random number generator based on high-quality Rydberg single-photon source. Our experimental results demonstrate the Wheeler’s nontrivial time order inversion in this quantum system and confirm the Copenhagen interpretation of the physical reality of quantum state, which means the particle/wave character can only be ascribed to a quantum system when it was measured. This work is encouraging toward testing the foundations of quantum mechanics using the Rydberg atoms.
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9

Vedovato, Francesco, Costantino Agnesi, Matteo Schiavon, Daniele Dequal, Luca Calderaro, Marco Tomasin, Davide G. Marangon, et al. "Extending Wheeler’s delayed-choice experiment to space." Science Advances 3, no. 10 (October 2017): e1701180. http://dx.doi.org/10.1126/sciadv.1701180.

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10

Michielsen, K., S. Yuan, S. Zhao, F. Jin, and H. De Raedt. "Coexistence of full which-path information and interference in Wheeler's delayed-choice experiment with photons." Physica E: Low-dimensional Systems and Nanostructures 42, no. 3 (January 2010): 348–53. http://dx.doi.org/10.1016/j.physe.2009.06.072.

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11

Kastner, R. E. "On Delayed Choice and Contingent Absorber Experiments." ISRN Mathematical Physics 2012 (November 30, 2012): 1–9. http://dx.doi.org/10.5402/2012/617291.

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It is pointed out that a slight variation on the Wheeler Delayed Choice Experiment presents the same challenge to orthodox quantum mechanics as Maudlin-type contingent absorber experiments present to the Transactional Interpretation (TI). Therefore, the latter cannot be used as a basis for refutation of TI.
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12

Boyd, Jeffrey H. "Rethinking a Wheeler delayed-choice gedanken experiment." Physics Essays 25, no. 3 (September 2012): 390–96. http://dx.doi.org/10.4006/0836-1398-25.3.390.

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13

Zhao, S., S. Yuan, H. De Raedt, and K. Michielsen. "Event-by-event simulation of Wheeler’s delayed-choice experiment." Physics Procedia 6 (2010): 27–30. http://dx.doi.org/10.1016/j.phpro.2010.09.024.

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14

UMAKANTHA, N. "A quantum potential approach to the Wheeler delayed-choice experiment." Nature 319, no. 6055 (February 1986): 699. http://dx.doi.org/10.1038/319699a0.

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15

BOHM, D. J., C. DEWDNEY, and B. H. HILEY. "A quantum potential approach to the Wheeler delayed-choice experiment." Nature 319, no. 6055 (February 1986): 699. http://dx.doi.org/10.1038/319699b0.

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16

Bohm, D. J., C. Dewdney, and B. H. Hiley. "A quantum potential approach to the Wheeler delayed-choice experiment." Nature 315, no. 6017 (May 1985): 294–97. http://dx.doi.org/10.1038/315294a0.

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17

Kaloyerou, P. N. "A field-theoretic causal model of a Mach–Zehnder Wheeler delayed-choice experiment." Physica A: Statistical Mechanics and its Applications 355, no. 2-4 (September 2005): 297–318. http://dx.doi.org/10.1016/j.physa.2005.02.059.

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18

Melkikh, Alexey V. "Quantum entanglement, Wheeler’s delayed choice experiment and its explanation on the basis of quantization of fields." Journal of Physics: Conference Series 880 (August 2017): 012030. http://dx.doi.org/10.1088/1742-6596/880/1/012030.

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19

Božić, M., L. Vušković, M. Davidović, and Á. S. Sanz. "On Wheeler's delayed-choice Gedankenexperiment and its laboratory realization." Physica Scripta T143 (February 1, 2011): 014007. http://dx.doi.org/10.1088/0031-8949/2011/t143/014007.

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20

Peruzzo, A., P. Shadbolt, N. Brunner, S. Popescu, and J. L. O'Brien. "A Quantum Delayed-Choice Experiment." Science 338, no. 6107 (November 1, 2012): 634–37. http://dx.doi.org/10.1126/science.1226719.

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21

Kaiser, F., T. Coudreau, P. Milman, D. B. Ostrowsky, and S. Tanzilli. "Entanglement-Enabled Delayed-Choice Experiment." Science 338, no. 6107 (November 1, 2012): 637–40. http://dx.doi.org/10.1126/science.1226755.

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22

Bendahane, M., M. El Atiki, and A. Kassou-Ou-Ali. "The Quantum Delayed Choice Experiment Revisited." Brazilian Journal of Physics 50, no. 1 (December 6, 2019): 52–56. http://dx.doi.org/10.1007/s13538-019-00722-0.

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23

Sun, Jun, Yong-Nan Sun, Chuan-Feng Li, and Guang-Can Guo. "On Delay of the Delayed Choice Experiment." Chinese Physics Letters 32, no. 9 (September 2015): 090302. http://dx.doi.org/10.1088/0256-307x/32/9/090302.

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24

Fankhauser, Johannes. "Taming the Delayed Choice Quantum Eraser." Quanta 8, no. 1 (August 11, 2019): 44–56. http://dx.doi.org/10.12743/quanta.v8i1.88.

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I discuss the delayed choice quantum eraser experiment by drawing an analogy to a Bell-type measurement and giving a straightforward account in standard quantum mechanics. The delayed choice quantum eraser experiment turns out to resemble a Bell-type scenario in which the resolution of the paradox is rather trivial, and so there really is no mystery. At first glance, the experiment suggests that measurements on one part of an entangled photon pair (the idler) can be employed to control whether the measurement outcome of the other part of the photon pair (the signal) produces interference fringes at a screen after being sent through a double slit. Significantly, the choice whether there is interference or not can be made long after the signal photon encounters the screen. The results of the experiment have been alleged to invoke some sort of backwards in time influence. I argue that this issue can be eliminated by taking into proper account the role of the signal photon. Likewise, in the de Broglie–Bohm picture the trajectories of the particle can be given a well-defined description at any instant of time during the experiment. Thus, it is again clear that there is no need to resort to any kind of backwards in time influence.Quanta 2019; 8: 44-56.
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25

Guo, Qi, Liu-Yong Cheng, Hong-Fu Wang, and Shou Zhang. "Quantum Delayed-Choice Experiment and Wave-Particle Superposition." International Journal of Theoretical Physics 54, no. 8 (December 28, 2014): 2517–23. http://dx.doi.org/10.1007/s10773-014-2482-1.

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26

Wang, Kai, Qian Xu, Shining Zhu, and Xiao-song Ma. "Quantum wave–particle superposition in a delayed-choice experiment." Nature Photonics 13, no. 12 (September 2, 2019): 872–77. http://dx.doi.org/10.1038/s41566-019-0509-0.

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27

Li, Gang, Pengfei Zhang, and Tiancai Zhang. "Quantum delayed-choice experiment with a single neutral atom." Optics Letters 42, no. 19 (September 21, 2017): 3800. http://dx.doi.org/10.1364/ol.42.003800.

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28

Kawai, Takeshi, Toru Ebisawa, Seiji Tasaki, Masahiro Hino, Dai Yamazaki, Hiroshi Tahata, Tsunekazu Akiyoshi, Yoko Matsumoto, Norio Achiwa, and Yoshie Otake. "Development of cold neutron pulser for delayed choice experiment." Physica B: Condensed Matter 241-243 (December 1997): 133–35. http://dx.doi.org/10.1016/s0921-4526(97)00530-9.

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29

Boyd, Jeffrey H. "Rethinking Alain Aspect's 1982 Bell test experiment with delayed choice." Physics Essays 26, no. 4 (December 30, 2013): 582–91. http://dx.doi.org/10.4006/0836-1398-26.4.582.

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30

Liu, Ke, Yuan Xu, Weiting Wang, Shi-Biao Zheng, Tanay Roy, Suman Kundu, Madhavi Chand, et al. "A twofold quantum delayed-choice experiment in a superconducting circuit." Science Advances 3, no. 5 (May 2017): e1603159. http://dx.doi.org/10.1126/sciadv.1603159.

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31

Donker, Hylke C., Hans De Raedt, and Kristel Michielsen. "Event-by-event simulation of a quantum delayed-choice experiment." Computer Physics Communications 185, no. 12 (December 2014): 3109–18. http://dx.doi.org/10.1016/j.cpc.2014.08.001.

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32

Boyd, Jeffrey H. "Rethinking a delayed choice quantum eraser experiment: A simple baseball model." Physics Essays 26, no. 1 (March 1, 2013): 100–109. http://dx.doi.org/10.4006/0836-1398-26.1.100.

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33

Wang, Kai, Qian Xu, Shining Zhu, and Xiao-song Ma. "Author Correction: Quantum wave–particle superposition in a delayed-choice experiment." Nature Photonics 14, no. 9 (April 28, 2020): 591. http://dx.doi.org/10.1038/s41566-020-0643-8.

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34

Filgueiras, J. G., R. S. Sarthour, A. M. Souza, I. S. Oliveira, R. M. Serra, and L. C. Céleri. "Quantum delayed-choice experiment in an environment with arbitrary white noise." Journal of Physics A: Mathematical and Theoretical 46, no. 24 (May 24, 2013): 245301. http://dx.doi.org/10.1088/1751-8113/46/24/245301.

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35

Baldzuhn, J., E. Mohler, and W. Martienssen. "A wave-particle delayed-choice experiment with a single-photon state." Zeitschrift f�r Physik B Condensed Matter 77, no. 2 (June 1989): 347–52. http://dx.doi.org/10.1007/bf01313681.

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36

Castrillón, Jhonny, Enrique J. Galvez, Boris A. Rodriguez, and Omar Calderón-Losada. "A time-energy delayed-choice interference experiment for the undergraduate laboratory." European Journal of Physics 40, no. 5 (August 20, 2019): 055401. http://dx.doi.org/10.1088/1361-6404/ab2afc.

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37

Bell, J. S. "De Broglie-Bohm, delayed-choice, double-slit experiment, and density matrix." International Journal of Quantum Chemistry 18, S14 (June 19, 2009): 155–59. http://dx.doi.org/10.1002/qua.560180819.

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38

Ding, Zhuolei, Ting Jiang, Chuansheng Chen, Vishnu P. Murty, Jingming Xue, and Mingxia Zhang. "The effect of choice on intentional and incidental memory." Learning & Memory 28, no. 12 (November 15, 2021): 440–44. http://dx.doi.org/10.1101/lm.053433.121.

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Recent studies have revealed that memory performance is better when participants have the opportunity to make a choice regarding the experimental task (choice condition) than when they do not have such a choice (fixed condition). These studies, however, used intentional memory tasks, leaving open the question whether the choice effect also applies to incidental memory. In the current study, we first repeated the choice effect on the 24-h delayed intentional memory performance (experiment 1). Next, using an incidental paradigm in which participants were asked to judge the category of the items instead of intentionally memorizing them, we observed the choice effect on judgment during encoding and memory performance in a 24-h delayed surprise test (experiment 2). Participants judged more accurately and quickly and had better recognition memory for items in the choice condition than for items in the fixed condition. These results are discussed in terms of the role of choice in both intentional and incidental memory.
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39

Morimoto, Masahito. "UNOBSERVABLE POTENTIALS TO EXPLAIN A QUANTUM ERASER AND A DELAYED-CHOICE EXPERIMENT." Progress In Electromagnetics Research M 62 (2017): 111–22. http://dx.doi.org/10.2528/pierm17082201.

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40

Ingraham, R. L. "Quantum nonlocality in a delayed-choice experiment with partial, controllable memory erasing." Physical Review A 50, no. 6 (December 1, 1994): 4502–5. http://dx.doi.org/10.1103/physreva.50.4502.

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41

Kawai, Takeshi, Toru Ebisawa, Seiji Tasaki, Masahiro Hino, Dai Yamazaki, Tsunekazu Akiyoshi, Yoko Matsumoto, Norio Achiwa, and Yoshie Otake. "Realization of a delayed choice experiment using a multilayer cold neutron pulser." Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 410, no. 2 (June 1998): 259–63. http://dx.doi.org/10.1016/s0168-9002(98)00263-0.

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42

F. Münte, Thomas, Zheng Ye, Josep Marco-Pallarés, Ulrike M. Krämer, Rebecca Schüle, Ludger Schöls, Nuria Rojo-Fite, et al. "Dopamine and intertemporal choice in humans." Zeitschrift für Neuropsychologie 29, no. 2 (May 1, 2018): 81–88. http://dx.doi.org/10.1024/1016-264x/a000218.

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Abstract. The dopamine (DA) system has been implicated in the mediation of cost/benefit evaluations involved in the intertemporal choices between immediate and delayed rewards. This involvement was further investigated in two studies of normal participants that had to decide between a smaller immediate and a larger delayed reward in a series of 27 decisions.In study 1 the dopamine D2/D3 receptor agonist pramipexole or placebo were administered in a double-blind cross-over protocol prior to the decisions. In study 2 the same experiment was conducted in two groups of normal participants that were homozygous for either the 7repeat or the 4 repeat variant of the exon III polymorphism of the Dopamine D4 receptor gene. Dopaminergic involvement is highlighted by the results.
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43

Jones, J. B., A. J. F. Webster, and C. M. Wathes. "A delayed aversion to atmospheric ammonia in Pigs." Proceedings of the British Society of Animal Science 1997 (1997): 115. http://dx.doi.org/10.1017/s1752756200595568.

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Intensively housed pigs are continuously exposed to aerial pollutants, such as ammonia gas (e.g. Robertson 1994). The objective of this study was to determine if exposure to ammonia, for an extended period, was aversive to a pig. The three chronic choice test experiments catalogued the behavioural responses of Duroc x Landrace pigs to concentrations of ammonia recorded frequently in commercial piggeries. The first experiment established if ammonia was aversive. The remaining experiments indirectly and directly traded off the strength of any aversion against thermal comfort. In the second experiment thermal comfort could be obtained either in the absence or presence of ammonia; in the third experiment thermal comfort could only be gained in the presence of ammonia.
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44

Deschuyteneer, Maud, André Vandierendonck, and Isabel Muyllaert. "Does Solution of Mental Arithmetic Problems Such as 2 + 6 and 3 × 8 Rely on the Process of “Memory Updating”?" Experimental Psychology 53, no. 3 (January 2006): 198–208. http://dx.doi.org/10.1027/1618-3169.53.3.198.

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Two experiments are reported that used the selective interference paradigm to study whether, besides response selection, the process of memory updating is involved in simple mental arithmetic. Participants were asked to solve simple sums (e.g., 2 + 6, Experiment 1) or simple products (e.g., 3 × 8, Experiment 2) in a single-task control condition and in three dual-task conditions with a selective interference task, simple reactions, choice reactions, or delayed choice reactions. The role of memory updating was estimated on the basis of the difference in impairment due to the choice reaction time and the delayed choice reaction time task, whereas the difference in impairment between the simple reaction time and the choice reaction time task indicates the role of response selection. While replicating previous results concerning response selection ( Deschuyteneer & Vandierendonck, 2005 , in press ), the study showed that memory updating is strongly involved in solving simple mental arithmetic sums and products.
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45

Morrell, Liz, James Buchanan, Laurence S. J. Roope, Koen B. Pouwels, Christopher C. Butler, Benedict Hayhoe, Sarah Tonkin-Crine, et al. "Public preferences for delayed or immediate antibiotic prescriptions in UK primary care: A choice experiment." PLOS Medicine 18, no. 8 (August 30, 2021): e1003737. http://dx.doi.org/10.1371/journal.pmed.1003737.

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Background Delayed (or “backup”) antibiotic prescription, where the patient is given a prescription but advised to delay initiating antibiotics, has been shown to be effective in reducing antibiotic use in primary care. However, this strategy is not widely used in the United Kingdom. This study aimed to identify factors influencing preferences among the UK public for delayed prescription, and understand their relative importance, to help increase appropriate use of this prescribing option. Methods and findings We conducted an online choice experiment in 2 UK general population samples: adults and parents of children under 18 years. Respondents were presented with 12 scenarios in which they, or their child, might need antibiotics for a respiratory tract infection (RTI) and asked to choose either an immediate or a delayed prescription. Scenarios were described by 7 attributes. Data were collected between November 2018 and February 2019. Respondent preferences were modelled using mixed-effects logistic regression. The survey was completed by 802 adults and 801 parents (75% of those who opened the survey). The samples reflected the UK population in age, sex, ethnicity, and country of residence. The most important determinant of respondent choice was symptom severity, especially for cough-related symptoms. In the adult sample, the probability of choosing delayed prescription was 0.53 (95% confidence interval (CI) 0.50 to 0.56, p < 0.001) for a chesty cough and runny nose compared to 0.30 (0.28 to 0.33, p < 0.001) for a chesty cough with fever, 0.47 (0.44 to 0.50, p < 0.001) for sore throat with swollen glands, and 0.37 (0.34 to 0.39, p < 0.001) for sore throat, swollen glands, and fever. Respondents were less likely to choose delayed prescription with increasing duration of illness (odds ratio (OR) 0.94 (0.92 to 0.96, p < 0.001)). Probabilities of choosing delayed prescription were similar for parents considering treatment for a child (44% of choices versus 42% for adults, p = 0.04). However, parents differed from the adult sample in showing a more marked reduction in choice of the delayed prescription with increasing duration of illness (OR 0.83 (0.80 to 0.87) versus 0.94 (0.92 to 0.96) for adults, p for heterogeneity p < 0.001) and a smaller effect of disruption of usual activities (OR 0.96 (0.95 to 0.97) versus 0.93 (0.92 to 0.94) for adults, p for heterogeneity p < 0.001). Females were more likely to choose a delayed prescription than males for minor symptoms, particularly minor cough (probability 0.62 (0.58 to 0.66, p < 0.001) for females and 0.45 (0.41 to 0.48, p < 0.001) for males). Older people, those with a good understanding of antibiotics, and those who had not used antibiotics recently showed similar patterns of preferences. Study limitations include its hypothetical nature, which may not reflect real-life behaviour; the absence of a “no prescription” option; and the possibility that study respondents may not represent the views of population groups who are typically underrepresented in online surveys. Conclusions This study found that delayed prescription appears to be an acceptable approach to reducing antibiotic consumption. Certain groups appear to be more amenable to delayed prescription, suggesting particular opportunities for increased use of this strategy. Prescribing choices for sore throat may need additional explanation to ensure patient acceptance, and parents in particular may benefit from reassurance about the usual duration of these illnesses.
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46

常, 炳功. "Interpretation of Double-Slit Experiment by Space-Time Ladder Theory—Essence of Delayed Choice Quantum Eraser Experiment." Modern Physics 09, no. 06 (2019): 247–62. http://dx.doi.org/10.12677/mp.2019.96025.

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47

Hamza, Danish Ali, Tasawar Abbas, Muhammad Asjad, Muhammad Imran, and Rameez-ul-Islam. "Observing wave–particle behavior of entangled atoms in cavity assisted delayed-choice experiment." Journal of Mathematical Physics 63, no. 3 (March 1, 2022): 032103. http://dx.doi.org/10.1063/5.0080586.

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A scheme is proposed to study the wave–particle duality of two entangled atoms in a cavity-QED framework. Two atoms may exhibit a mutating trend between particle and wave behaviors. This mutating behavior can be post-selected after the atomic states have been recorded on the state selective detectors. In the present proposal, second Hadamard transformation is always present, whereas the probabilities are the same as that in the case, where the state of the second Hadamard can be controlled by an ancilla. The whole scheme revolves around resonant, off-resonant, and Ramsey interactions of two level atoms with the field. To observe the desired behavior, cavity assisted atom-field multiple swappings are employed for tagging as well as for the better control and good fidelity.
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48

Ingraham, R. L. "Erratum: Quantum nonlocality in a delayed-choice experiment with partial, controllable memory erasing." Physical Review A 51, no. 5 (May 1, 1995): 4295. http://dx.doi.org/10.1103/physreva.51.4295.3.

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49

de Almeida, N. G., A. T. Avelar, and W. B. Cardoso. "A proposal to implement a quantum delayed choice experiment assisted by cavity QED." Physics Letters A 378, no. 18-19 (March 2014): 1254–57. http://dx.doi.org/10.1016/j.physleta.2014.03.012.

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50

Diker, Firat. "Mathematical Relation between Concurrence and Intensity of a Photon in the Quantum Delayed-Choice Experiment." Journal of Physics: Conference Series 2148, no. 1 (December 1, 2021): 012010. http://dx.doi.org/10.1088/1742-6596/2148/1/012010.

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Abstract I provide the explicit mathematical expression of the correlation between concurrence and the intensity of a photon in the quantum delayed-choice experiment. This shows us that one may observe the wave-particle duality and entanglement simultaneously.
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