Cryptography aims to secure communication. Eve should not be able to eavesdrop on the communication between Alice and Bob. Quantum cryptography is 100% secure in as far as the physics is concerned. However, it is unsatisfying if this security is merely promised by a still new and even partially controversial theory. Who wants to trust their most important secrets to something that may be wrong? I am indebted to Matthew Saul Leifer, a researcher in the field of quantum information at the Perimeter Institute for Theoretical Physics, because the way he formulated it to me helps understanding the gravity and centrality of the issue. Leifer wrote:
“…there is no piece of information shorter than my entire bit string that the eavesdropper could know that would enable her to predict it. What guarantees that this is true, …one would want to be able to answer this question independently of the specifics of quantum theory. …” [private communication, emphasis added]
Can there be a completely reliable reason that guarantees that a sequence, for example the key used in quantum communication, Matthew’s bit string such as 01101010011010, is unknown? There is, and it is indeed “independent of the specifics of quantum theory,” because the aspect that guarantees it is pre-quantum. The reason does therefore not depend on the precise magnitude of the quantum violation of the Bell inequality for example, which is Matt's "specifics of quantum theory."
The cutting edge of quantum mechanics is quantum information theory. Robust quantum computing is still unavailable, but quantum cryptography is an application today. Quantum cryptography is the widely visible ‘proof-beyond-doubt’ for quantum physics. This is similar to your car’s GPS, which would not work without GPS satellites’ signals being adjusted according to Einstein’s general relativity. Your car's GPS system is in that sense the best proof of that general relativity is true that you have.
For quantum physics, similar holds. Atomic electron orbits and photons and all of that are in some sense rather misleading, because quantization is usually a rather than the core of quantum physics. Even quantum superposition is usually misunderstood in terms of a statistical mechanics paradigm that stays unaware of the profound nature of quantum correlations. In other words: they are not convincing, and doubters still hope for non-quantum substitutes such as ‘real local hidden variables’ to explain all observations in ways that do not need the weirder aspects of modern physics. Quantum cryptography however, through its application of quantum entanglement over long distances, forces us to accept apparent quantum non-locality, which is a “ ” effect, or as the specialists know it: Everett relativity with standard Bell violation.
The parallel worlds or ‘relative actualization’ description, which is not only empirically proven but anyway metaphysically self-evident, answers the core question of quantum cryptography. How so? How does ‘many-worlds/minds’ guarantee (as Matt demands in the quote) that something such as a bit-string-key used in quantum cryptography, a bit string like 01110100101001 used by Alice and Bob, remains unknown?
The claim seems immediately silly: If anybody knows, one can never be sure that somebody else does not also somehow know! But rather than this being the destruction of the argument, it is the very pillar on which the argument is rock solid. Parallel worlds ensure that not even Alice and Bob know, because all possible ones are there together!
Many-worlds is like a pack of poker cards. If Alice hands Bob a particular card as the cryptography key, say the Seven of Hearts, Eve in the middle can potentially look at it. Quantum correlation allows Alice to hand the full pack to Bob. She gives him only one card, but that card is blank, or better, it turns out to be a particular card of all possible ones only when looking at it. Quantum entanglement ensures that if Alice and Bob use the key like that, the “parallel world” of the Seven of Hearts of Alice is and stays paired up with the Seven of Hearts Bob possibility, and the King of Spade Alice pairs up with the King of Spade Bob potential world, and so on, such that all the Alice-Bob pairs use the same key on both ends. However, for Eve in the middle (and everybody else), all the cards are still in the game. If Eve looks at the blank card in order to know the key, Alice’s worlds pair up with Eve’s worlds instead, and so Bob only receives nonsense, because Bobs’ worlds are not paired up correctly anymore, the key does not fit, and so Bob (all of them except for a tiny fraction of unlucky ones in standard quantum mechanics) knows that the message has been intercepted and he stops communicating immediately.
Notice a very important distinction here: Many-worlds (1), which is pre-quantum, guarantees that all the cards can be in the game together, which guaranties that no particular card can be known. Quantum correlation (2) assures that Alice can give the whole pack of cards to Bob, namely via one blank card that is not looked at.
The first and more fundamental, namely Many-worlds, “guarantees” (as Matt demands) that quantum cryptography can be 100% secure; while the second, Matt's “specifics of quantum” correlation between the parallel worlds is what gives her access to the many-worlds, to the pack of cards.
The communication works the same as the correlation between Alice and Bob in the Einstein-Podolsky-Rosen paradox: In EPR, there are all the possible Alices, namely those that observe outcome zero and those that observe outcome one. There are also all the possible Bobs, those that see their own photon appear in channel zero or channel one. At a certain angle in the setup, the zero-Alices will pair only with one-Bobs, and one-Alices only with zero-Bobs, so that the combined observations of zero-zero or of one-one never occur. In the EPR experiment it is easily understood that if Eve should interfere, zero-zero and one-one measurements will occur, and so her eavesdropping cannot stay secret.
Matt pointed out that quantum cryptography has only been proven secure in case there is ‘non-signaling’. What he means, in more widely understood terms, is that when Einstein relativity and its speed of light velocity limit were to be shown fundamental, only then quantum cryptography would be 100% guaranteed to be secure. That is why the connection to the EPR issue is so important.
One can of course not claim that all the many (potentially wrong) quantum communication protocols now discussed in various venues are all secure, or thsat any system somebody sells you is secure. However, those protocols that stick correctly to an EPR-like setup are fundamentally secure, because Einstein relativity has been shown to be fundamental and EPR-like setups make use of the many-worldly aspect of physical totality in the correct way. If there is no particular sequence, all the possible sequences are involved in the secured communication, just like all the possible cats are teleported in superposition in quantum teleportation.
With quantum cryptography, a sequence of ones and zeros is entangled in such a way that not even Alice looks at it. This ensures not only that she herself does not know, but that there is no such certain sequence that could be known. All the possible sequences are still equivalently there together in superposition. There truly is no certain sequence that Eve can know.
This guarantee is independent of the specifics of quantum theory. The many-worlds description is pre-quantum and there are non-quantum many-worlds models (you could call them classical many-worlds models). What makes a many-world theory a quantum theory is how the different worlds statistically correlate with each other. Those details are necessary so that we can exploit the quantum relations in cryptography. This having access to several poker cards at once is is however different from there being different cards in parallel together in the first place. It is the latter aspect, the classical many-worlds nature, that guarantees that there is no particular card that can be known at that point.
Those who hold that only one world is real, that only one key is actualized, must think that the sequence of ones and zeros is a single, particular one, such as 100010101. Even if Alice does not know it in the sense of being able to tell you the sequence, she together with her apparatus constitutes a physical system, and this system “knows,” the absolute realists believe. Somewhere inside that physical system, there is the knowledge about the one real sequence hidden. If so, Eve may somehow be able to extract the vital parts.
The parallel-worlds aspect destroys this physical “knowledge,” because there is no such one Alice either. There are all the possible Alices with all the possible sequences, and as long as Bob(s) or Eve(s) do not look at the sequence, there is no such certain sequence that can be known. All the possible sequences are still in the game, and that is why Bob will find out whether Eve “looked at” the sequence, because her looking is actually her parallel worlds pairing up with those of Alice, and that pairing changes the correlations between the possible Alices and possible Bobs.
How shall I end this piece without ending apruptly? Again and again, for the most profound core aspects of the most cutting edge physics we are still today brought back to Einstein’s insights as the place were they are answered. Although Einstein rejected many-worlds, with the cutting edge of quantum theory, it was the mere proof of ‘non-signaling’ that was missing, and that is Einstein's territory. That proof requires no input of quantum physics whatsoever, and so the core question of quantum theory has been finally answered.