Do the laws of physics prohibit counterfactual communication?
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It has been conjectured that counterfactual communication is impossible, even for post-selected quantum particles. We challenge this by proposing exactly such a counterfactual scheme where---unambigiuously---none of Alice's photons has been to Bob. We demonstrate counterfactuality using a consistent histories approach as well as a weak measurement one. Crucially, the probability of Alice correctly learning Bob's bit can be made arbitrarily close to one, with no possible trace whatsoever left by Bob on Alice's photon.
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