More questions about reality and the security of quantum protocols
My lecture today in my Quantum Cryptography course brought together several recent threads on this blog. In particular, several interesting questions arose during the course of the lecture (I love having engaged and motivated students). The questions arose from our discussion of the BB84 protocol and the No-Cloning theorem. Essentially: 1. Do Alice and Bob need to be people or can they be machines? and 2. In what instances can Eve impersonate Bob (or Alice, for that matter)?
1. One student remarked that after studying it via the homework, lecture, etc., it seemed as if the BB84 protocol’s success was directly linked to the need for a human on either end interpreting the results. Essentially, she said, it seemed Alice and Bob had to be people as opposed to machines since it seems Eve might be able to fool Alice into thinking she’s really Bob if Alice was simply a machine. So, while she couldn’t necessarily clone Alice’s state before sending it back on to Bob, she might be able to pretend to be Bob. Notice that the answer to the first part of this question is at least partially related to the Chinese room argument I recently commented on.
2. After a bit of classroom discussion, one of my colleagues in the chemistry department who is sitting in on my lectures, noted that this seemed to indicate two different situations. So, if they’re all people, it is entirely possible for Eve to sneak up on Bob, slit his throat or take him hostage, and impersonate him. Quantum mechanics can never get around basic human espionage. But the question is, could there be a way for Eve to impersonate Bob (or perhaps Alice) without something quite as nefarious happening? For instance, someone in class suggested making a copy of Bob’s (or Alice’s) computer. Classically, this could be done (copying information off of a hard drive, for example) and is the basis of the argument many critics made concerning the use of quantum cryptography in the Swiss elections since, in this sense, copying a classical computer is essentially hacking.
In response to the latter, the answer would be different if the computers themselves were quantum. The No-Cloning theorem basically says that it’s perfectly ok to copy states if they’re orthogonal to one another, but if they are they have classical analogues and so you’re not really doing anything unusual. Because quantum computers make use of non-orthogonal states, the No-Cloning theorem implies you could never copy the hard drive of a quantum computer (at least perfectly). Note that it is potentially possible for a single qubit to be copied if you guess correctly (or already know) what state it is in. If you’re still not clear on this point, I would recommend Loepp & Wootters’ book Protecting Information.
So, Eve is left with only nefarious human means by which to obtain information from Alice and Bob. That still does not answer the question of whether or not Alice and Bob must be humans or not (i.e. whether they can be computers), but I think this is a question that combines quantum information theory with questions of artificial intelligence. Anyone out there got any thoughts on this subject?