How Quantum is Quantum Counterfactual Communication?

Abstract

Quantum Counterfactual Communication is the recently-proposed idea of using quantum mechanics to send messages between two parties, without any particles travelling between them. While this has excited massive interest, both for potential 'un-hackable' communication, and insight into the foundations of quantum mechanics, it has been asked whether this phenomena is truly quantum, or could be performed classically. We examine counterfactuality, both classical and quantum, and the protocols proposed so far, and conclude it must be quantum, at least insofar as it requires particle quantisation.

Could wavefunctions simultaneously represent knowledge and reality?

“…This is unlike quantum 'probability amplitudes', which are really quasiprobabilities -they can be negative or even imaginary, and so can interfere destructively with one another. This negative probability interference is a key part of quantum mechanics, explaining peculiar phenomena such as the sequential Stern-Gerlach experiment [33], the Elitzur-Vaidman Bomb Detector [34], and counterfactual communication [35,36] and imaging [37]. It is unclear how the real non-negative probabilities of this real underlying state-of-the-world could replicate these effects -casting doubt on this framework.…”

Realizing the "fictitious" beam splitter -- A stationary implementation of semi-counterfactual interaction-free imaging

“…Also, if a photon left a weak trace in the path x N z (e.g., in the apparatus proposed in Ref. [6]), it is arguable whether we can still call it counterfactual even when the photon is finally found by D (i) 1 [7,8,11,12,[14][15][16]22]. Thus it may be safer to call the whole process "semicounterfactual".…”

“…In 2009, basing on similar ideas, Noh proposed a more ingenious setup of the interferometer and applied it to quantum key distribution (QKD) [3]. It immediately caught great interests, most of which focused on whether there can be fully counterfactual protocols for transferring classical [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] or quantum information [23][24][25][26][27].…”

Counterfactual Ghost Imaging

“…Counterfactuality, an extension of Interaction-Free Measurement, is the idea of using quantum effects to either probe objects or send messages without any matter/energy passing between the two parties when information is transferred [12]. This is based on Elitzur and Vaidman's Interaction-Free Bomb Detector [13], where a bomb, set to trigger on detecting the presence of a single photon, is put in one of the arms of a Mach-Zehnder in-FIG.…”

“…Zhang et al combined Ghost Imaging with the Elitzur-Vaidman Bomb Detector [13] to create a form of Ghost Imaging where there is a chance that information is still received about the imaged object without any photons being absorbed by it [23]. However, the Elitzur-Vaidman Bomb Detector is not always necessarily counterfactual -there is a (reasonably high) chance the photon can go via the object being investigated [12]. By replacing the Elitzur-Vaidman object-detection system in Zhang's protocol with Salih et al's method for counterfactual communication, we create a protocol for ghost imaging that is always counterfactual -whenever information is received about the imaged object, no photons have interacted with that object.…”