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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. 

Abstract Ammonium vanadate with bronze structure (NH 4 V 4 O 10 ) is a promising cathode material for zinc-ion batteries due to its high specific capacity and low cost. However, the extraction of $${\text{NH}}_{{4}}^{ + }$$ NH 4 + at a high voltage during charge/discharge processes leads to irreversible reaction and structure degradation. In this work, partial $${\text{NH}}_{{4}}^{ + }$$ NH 4 + ions were pre-removed from NH 4 V 4 O 10 through heat treatment; NH 4 V 4 O 10 nanosheets were directly grown on carbon cloth through hydrothermal method. Deficient NH 4 V 4 O 10 (denoted as NVO), with enlarged interlayer spacing, facilitated fast zinc ions transport and high storage capacity and ensured the highly reversible electrochemical reaction and the good stability of layered structure. The NVO nanosheets delivered a high specific capacity of 457 mAh g −1 at a current density of 100 mA g −1 and a capacity retention of 81% over 1000 cycles at 2 A g −1 . The initial Coulombic efficiency of NVO could reach up to 97% compared to 85% of NH 4 V 4 O 10 and maintain almost 100% during cycling, indicating the high reaction reversibility in NVO electrode.