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Counterfactual quantum cryptography (CQC) is used here as a tool to assess the status of the quantum state: Is it real/ontic (an objective state of Nature) or epistemic (a state of the observer’s knowledge)? In contrast to recent approaches to wave function ontology, that are based on realist models of quantum theory, here we recast the question as a problem of communication between a sender (Bob), who uses interaction-free measurements, and a receiver (Alice), who observes an interference pattern in a Mach-Zehnder set-up. An advantage of our approach is that it allows us to define the concept of “physical”, apart from “real”. In instances of counterfactual quantum communication, reality is ascribed to the interaction-freely measured wave function (ψ) because Alice deterministically infers Bob’s measurement. On the other hand, ψ does not correspond to the physical transmission of a particle because it produced no detection on Bob’s apparatus. We therefore conclude that the wave function in this case (and by extension, generally) is real, but not physical. Characteristically for classical phenomena, the reality and physicality of objects are equivalent, whereas for quantum phenomena, the former is strictly weaker. As a concrete application of this idea, the nonphysical reality of the wavefunction is shown to be the basic nonclassical phenomenon that underlies the security of CQC.(2)
Intuition from our everyday lives gives rise to the belief that information exchanged between remote parties is carried by physical particles. Surprisingly, in a recent theoretical study [Salih H, Li ZH, Al-Amri M, Zubairy MS (2013) Phys Rev Lett 110:170502], quantum mechanics was found to allow for communication, even without the actual transmission of physical particles. From the viewpoint of communication, this mystery stems from a (nonintuitive) fundamental concept in quantum mechanics—wave-particle duality. All particles can be described fully by wave functions. To determine whether light appears in a channel, one refers to the amplitude of its wave function. However, in counterfactual communication, information is carried by the phase part of the wave function. Using a single-photon source, we experimentally demonstrate the counterfactual communication and successfully transfer a monochrome bitmap from one location to another by using a nested version of the quantum Zeno effect.(3)
1. A distant star emits a photon many billions of years ago.
2. The photon must pass a dense galaxy (or black hole) directly in its path toward earth.
"Gravitational lensing" predicted by general relativity (and well verified) will make the light bend around the galaxy or black hole. The same photon can, therefore, take either of two paths around the galaxy and still reach earth. It can take the left path and bend back toward earth; or it can take the right path and bend back toward earth. Bending around the left side is the experimental equivalent of going through the left slit of a barrier; bending around the right side is the equivalent of going through the right slit.
3. The photon continues for a very long time (perhaps a few more billion years) on its way toward earth.
4. On earth (many billions of years later), an astronomer chooses to use a screen type of light projector, encompassing both sides of the intervening and the surrounding space without focusing or distinguishing among regions. The photon will land somewhere along the field of focus without our astronomer being able to tell which side of the galaxy/black hole the photon passed, left or right. So the distribution pattern of the photon (even of a single photon, but easily recognizable after a lot of photons are collected) will be an interference pattern.
5. Alternatively, based on what she had for breakfast, our astronomer might choose to use a binocular apparatus, with one side of the binoculars (one telescope) focused exclusively on the left side of the intervening galaxy, and the other side focussed exclusively on the right side of the intervening galaxy. In that case the "pattern" will be a clump of photons at one side, and a clump of photons at the other side.
Now, for many billions of years the photon is in transit in region 3. Yet we can choose (many billions of years later) which experimental set up to employ, the single wide-focus, or the two narrowly focused instruments.(4)
Of course, the status of the wave function (as being real or epistemic) does not depend on Bob’s choice of AB or FB. Nor does it depend on whether Bob is located at the end of arm a or b. What may conclude is that the each of the superposed states in Eq. (1), ψa ≡ a † |0, 0i and ψb ≡ b † |0, 0i, is by itself real-nonphysical, and thus, so too the particle state state |Ψi = √ 1 2 (ψa + ψb) in Eq. (1) is also real-nonphysical. We may therefore conclude that the quantum state is quite generally real-nonphysical. In retrospect, we may reflect in this new light on the wisdom of Feynman’s observation with regard to the double-slit experiment, mentioned in the opening paragraph. Our approach suggests that in the production of fringes in the double-slit experiment, there is indeed some “real stuff” travelling down both slits, but it is not physical. This explication thus puts (or so we hope!) a name on the mystery alluded to by Feynman.
Our work showed that the non-physical reality of the wave function is not an abstruse philosophical notion, but has the concrete application of being responsible for security in CQC. Finally, we venture that it is the lack of distinction in the literature between the real and the physical aspect that is responsible for the historical difficulty in interpreting the physical significance of the quantum state. In the discussion pertaining to the double-slit experiment, at first one has the intuitive feeling that there is something real traveling down both slits. One then subconsciously maps this real thing to something physical. But clearly the possibility of the quantum wave as a physical entity is one that we would consciously reject. Thus, psychologically speaking, a person thinking about quantum foundations is caught in the perpetual dilemma of deciding whether or not the quantum state is real. It is our belief that our work resolves this dilemma.(2)