Quantum Information Seminar Series: Patrick Hayden
- Date: 03/14/2011
University of Washington
Uncertainty, encryption and low-distortion embeddings
Abstract: Where should one look to find bases satisfying strong
uncertainty relations? Position and momentum lead the way: it's hard to
do better than any orthonormal basis and its Fourier transform. The
natural generalization to so-called mutually unbiased bases, however,
leaves a bit to be desired when it comes to uncertainty relations.
Reframing the search in terms of low-distortion embeddings instead leads
to bases satisfying much stronger uncertainty relations than had
previously been known, plus a
wealth of applications. I'll explain, for example, how to encrypt an
n-bit message using a constant-sized secret key and how to perform
equality testing of quantum states using a a constant amount of quantum
communication. Based on joint work with Omar Fawzi and Pranab Sen.