Tuesday, April 9, 2013

No randomness on the fly

The MyCQstate blog gives a nice summary of attempts to use entanglement for cryptography, and
This credo is best exemplified by the use of entanglement in quantum information: ... This paradigm shift ...

This semester (or what remains of it) at MIT I am organizing a small reading group whose focus will be the study of entanglement as a resource for cryptography. ...

Bell identified the following three reasonable assumptions, that I’ll refer to as in the following:

1. Measurement independence (“free will”):...
2. No-signaling (“no violation of special relativity”): ...
3. Outcome independence (“local realism”):...

Although it was explicitly made only relatively recently (see Chapter 5 in Roger Colbeck’s 2009 Ph.D. thesis), the sole violation of any Bell inequality already has one striking consequence: any physical process whose input/output behavior generates said violation cannot by definition satisfy all three basic assumptions . Provided that we believe in free will (inputs in the experiment are chosen independently of the system’s internal state) and e.g. special relativity (as a way to enforce the no-signaling condition between the system’s two parts), then I claim that the physical process — whatever it is, quantum mechanical or not — must generate randomness on the fly.
Random numbers are useful in cryptography, so if quantum mechanics can find a way to generate and transmit randomness on the fly, then maybe there would be some use to cryptography.

Unfortunately no such application has been found. The problem is in the assumption of local realism, which means that observations must faithfully reflect hidden mathematical variables, and no such variables have been found. The concept of hidden variables is appealing to some people, but it is contrary to how quantum mechanics has been understood for 80 years.

Entanglement is not even necessary for quantum cryptography. See BB84 for an explanation of it without entanglement. So the emphasis on entanglement is misleading.

Quantum cryptography does not solve any problems that are not better solved with conventional cryptography, and has no practical use. The main drawbacks of quantum cryptography are its inability to use routers or provide authentication, in addition to the questionable security. I guess it is being used here as a way of explaining quantum mechanics, but even that it not correct if it is claimed that it generates randomness on the fly.

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