Quantum Information Seminar Series: Patrick Hayden

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. arXiv:1010.3007.