New decomposition for unitary matrices!

  • Imagine you are sipping tea or coffee while discussing various issues with a broad and diverse network of students, colleagues, and friends brought together by the common bond of physics, graduate school, and the physics GRE.

Posts: 381
Joined: Mon May 24, 2010 11:34 pm

New decomposition for unitary matrices!

Postby CarlBrannen » Wed Mar 30, 2011 12:22 pm

A conjecture about bases of finite n-dimensional Hilbert spaces appears to have finally been proved. Given two bases, it's always possible to choose a state that has equal transition probabilities to all the 2n basis states:

I've been working on this for three years. The guy who proved it is a Stanford math postdoc specializing in symplectic topology and Hamiltonian dynamics:

As soon as I get the (rather subtle I think) proof verified I'm going to rewrite a paper of mine and send it in to J. Math. Phys.:

The conjecture shows that the unitary group $U(n)$ can be described as the arbitrary complex phases acting on a subgroup which is isomorphic to $U(n-1)$. As such, it gives a recursive definition of the unitary matrices in terms of complex phases only.

Return to “Physics Lounge”

Who is online

Users browsing this forum: No registered users and 3 guests