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Here's my reasoning:

Setup 1: Take a traditional double slit experiment and turn on the photon source. Interference fringes should appear on a detector screen placed opposite the photon emitter, right?

Setup 2: The often cited "which-way" variation of the double slit experiment, in which extremely sensitive photon detectors are placed in the slits. These photon detectors are designed to allow the photons to pass, but to measure their passage. The interference fringes on the detector screen should no longer be present and the detectors placed at the slits should have a record of the passage of the individual photons.

Setup 3: A "which-way" variation with the photon emitter turned down so that it emits only 1 photon per second. The result, at least on the detection screen, of setup 3 should be the same as setup 2, just really, really dim. However, now that the rate of photons' emission and detection is drastically reduced and carefully controlled, there is an additional piece of information available. That information is the "time stamp" of each photon emission/detection event. Using that additional time-stamp information, correlations between the two slits can be recorded for each specific photon. For example, the measurements from slit A are recored by Alice and the measurements from slit B are recorded by Bob. Now, if I'm not mistaken, Alice and Bob should have a perfect one-time pad which can be used for unbreakable encryption.

I've heard of quantum entanglement enabling secure one-time pad distribution, but the photons in a double slit experiment are not necessarily entangled in the traditional sense. And yet, the combination of the time stamp information and the photon's necessarily complementary passage through only one of the two slits available would seem to imply that a secure one-time pad can be distributed (with proper planning and implementation), without the need for a shared source of entangled photons.

Does this third setup successfully produce (and distribute) a one-time pad? Is a key resulting from the described setup functionally equivalent to one produced via Quantum Key Distribution?

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  • $\begingroup$ A fewf issues: 1) there is no such thing as a photon detector that does not destroy the photon, the detector you mention was part of a thought experiment ( Einstein, Wheeler) but does not exist. 2) If you place a detector at the screen it may be possible that the times are not that predictable, for example slit 1 can send photos over to slit 2's side. 3) A single photon slow source becomes statistical in it's emission, it's not a steady source so timing could be tricky, that's likely your biggest issue. $\endgroup$
    – PhysicsDave
    Jul 14, 2019 at 3:25
  • $\begingroup$ single photon double slit sps.ch/en/articles/progresses/… . and a newer one aapt.scitation.org/doi/full/10.1119/1.4955173 $\endgroup$
    – anna v
    Jul 14, 2019 at 3:44
  • $\begingroup$ @ PhysicsDave: Engineering challenges my good man! Just Engineering challenges :-) It doesn't have to be photons. We could use electrons instead (phys.org/news/…). As far as the timing goes, NP, just slow the bitrate down to the point of absurdity. Say, turn the emitter on once per day and turn it off again as soon as it emits an electron. And since we're placing electron detectors in the slits, the screen is actually irrelevant. The quantum interference pattern is destroyed as soon as the detectors have detected the electron anyway. $\endgroup$
    – Thor
    Jul 14, 2019 at 4:29

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The point of (quantum) cryptography is not to just distribute a correlated random key between Alice and Bob, but to distribute a secure key, i.e. one which cannot be known to a potential attacker. Your scheme falls short in that regard: Nothing would prevent an attacker (who would substitute the photon source) to send photons prepared in such a way that they only arrive at one predetermined slit, rather than both with equal probability. Thus, such a key would look random to Alice and Bob, yet the eavesdropper would have perfect knowledge of the key.

Unless, of course, Alice and Bob have full control of the entire experimental setup. But then, again, they could also just toss a coin.

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  • $\begingroup$ Excellent points. As you point out, the setup as described would certainly be susceptible to an eavesdropper, unless of course Alice and Bob controlled the entire apparatus, which would negate the whole exercise. But what I actually asked was: 1) Does this third setup successfully produce (and distribute) a one-time pad? and 2) Is a key resulting from the described setup functionally equivalent to one produced via Quantum Key Distribution? $\endgroup$
    – Thor
    Jul 16, 2019 at 2:26
  • $\begingroup$ The reason I asked these questions, which, admittedly, I did include in my original post, was because I was considering the possibility of using an extremely distant shared source of photons, like a distant star or something (I have no idea if such a source could even exist in principle)... But I thought this question was a little too far out there for consideration on this forum, so I instead asked about the theoretical basis of this type of classical key distribution. $\endgroup$
    – Thor
    Jul 16, 2019 at 2:33
  • $\begingroup$ Lol! There you go, you earned it! $\endgroup$
    – Thor
    Jul 18, 2019 at 23:59

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