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We report an experimental realization of a modified counterfactual communication protocol that eliminates the dominant environmental trace left by photons passing through the transmission channel. Compared to Wheeler’s criterion for inferring past particle paths, as used in prior protocols, our trace criterion provides stronger support for the claim of the counterfactuality of the communication. We verify the lack of trace left by transmitted photons via tagging the propagation arms of an interferometric device by distinct frequency-shifts and finding that the collected photons have no frequency shift which corresponds to the transmission channel. As a proof of principle, we counterfactually transfer a quick response code image with sufficient fidelity to be scanned with a cell phone.
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A criterion for uniform finiteness in the imaginary sorts
Let T be a theory. If T eliminates ∃∞, it need not follow that Teq eliminates ∃∞, as shown by the example of the p-adics. We give a criterion to determine whether Teq eliminates ∃∞. Specifically, we show that Teq eliminates ∃∞ if and only if ∃∞ is eliminated on all interpretable sets of “unary imaginaries.” This criterion can be applied in cases where a full description of Teq is unknown. As an application, we show that Teq eliminates ∃∞ when T is a C-minimal expansion of ACVF.
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- Award ID(s):
- 1803120
- PAR ID:
- 10313370
- Date Published:
- Journal Name:
- Archive for Mathematical Logic
- ISSN:
- 0933-5846
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00153-021-00803-5
