## February 05, 2013

### No threat to quantum cryptography (at least from quirks of fluid mechanics)

A few days ago my colleague at University of Latvia,  +Andris Ambainis, has shown me a recent preprint by  +Ross Anderson and +Robert Brady. The title and the content of their paper are so provocative (e.g., "full range of quantum phenomena from completely classical motion" and "quantum cryptography is not probably secure") that it has understandably attracted some attention of the cryptography community and led to sensational news reports attributed to "Cambridge experts".

As a condensed matter physicist, I'd like to state a few things that I hope will quickly clarify this confusion.  Below are you will find a list of statements regarding  arXiv:1301.7351 by Anderson and Brady (A&B) and arXiv:1301.7540 by Brady. You don't have to trust me - run the list by any tenured physicist at your university/department.
1. There is no explicit model for entanglement (or any other kind of many-particle correlation) in Brady's "sonon" model of an electron or in the A&B preprint.
2. As a corollary, the model is irreconcilable with each of the myriad of experimental facts underlying our trust in the conventional quantum many-body theory (ie., Shcrodinger equation in Fock space). Explicitly:
1. Spectrum of any atom beyond hydrogen.
2. Superconductivity (from which Josephson-effect-based QIP is derived).
3. Anomalous value of electron's gyromagnetic ratio (which by itself long ago has fundamentally invalidated any single-particle approximation for the physical electron, including Dirac equation which Brady connects his model to).
4. Exchange interaction and ferromagnetism.
5. The Standard Model of particle physics.
3. Another corollary: in contrast to standard theory, A&B provide no alternative method to compute the outcome of any of Bell-inequality testing experiment.  (The latter belong the same myriad of experimental keyholes that quantum theory has successfully passed through).
4. Brady's use of the historical name "fine structure constant" for his estimate of the squared dimensionless Coulomb charge of the "sonon" ($\alpha < 1/49$) is misleading. There is no spin-orbit interaction in his model and hence no prediction for fine structure of atomic spectra.
One can go on and pick apart individual superficial analogies put forward by A&B that a non-specialist may mistake for valid criticism of contemporary quantum theory, but I hope that I have made it clear enough that scientific implications of the controversy stirred by A&B, if any, do not belong to the domain of physical sciences.