Mutually Unbiased Bases (MUB) and Lie Algebra June 15

Filed under Research by Oscar Boykin | 0 comments

Along with my co-authors Meera Sitharam, Pham Huu Tiep, and Pawel Wocjan, we have just posted a new paper to the Arxiv titled Mutually Unbiased Bases and Orthogonal Decompositions of Lie Algebras. This paper shows the connection between the problem of Mutually Unbiased Bases in quantum information, and the problem of orthogonal decompositions of Lie Algebras.

One new thing we learn from this connection is that any set of MUBs that are eigenvectors of a Monomial Matrix in dimension 6, then there can be at most 3 MUBs, which is equivalent to the “reduce-to-prime-power” approach. Interestingly, all known sets of MUBs are equivalent to eigenvectors of monomial matrices.

A New Kind of GNU/Linux June 1

Filed under Computing by Oscar Boykin | 1 comment

I would be very interested in a new kind of GNU/Linux distribution. For many people, maintaining a system is not something they would care to do. They do not want to be burdened with system administration or don’t have the skills to do the job properly. What I propose is something like the Linux Terminal Server Project for home users. I am not suggesting that the software run on a remote server and display locally, but that the systems boot from a remote NFS server. The software is run locally, but installed and maintained on a remote server.

Here is how the system works:

  • User obtains a boot-cd to start up his system (this is like an install disk).
  • Like a live-CD, the system automatically configures the hardware. But unlike a live-CD, the system makes use of the local disks.
    The first time the user starts the system, she is asked if she wants to use part of her disk to speed up performance (highly recommended), and if she would like to use part of the disk to keep her personal files. If the user says no, we are back into the normal live-CD mode, and forget everything, but if the user wants to use the disk, things can get interesting.
  • The disk is used for two things: caching a remote read-only NFS file system, and storing the users home directory. The CD contains the most recent snapshot of the remote NFS file system (or the most commonly used parth thereof).
  • The cache is initialized with the CD data.
  • From then on, the system runs all software from the server. An NFS caching mechanism makes sure not to transfer files if they are up to date in the local cache.

The user never installs any software, never does any updates, and never does any system administration. If there is some update that requires a reboot, a msg can be presented to the user to notify her to restart as soon as possible, but otherwise, such updates will take effect at the next boot.

This system is a dedicated desktop environment. As such, one can get rid of root completely.
Since hardware is configured automatically, and a huge selection of software is already installed, the user has no need or ability to do anything that requires root access (assuming we allow any local user to restart the computer).

This is apt-get without user intervention to get packages, or Click-N-Run except, just Run.

Clearly this is not for everyone, but for many home and corporate users, this system would be an easy to use, easy to maintain, cheap to deploy system. If it has all the Debian Packages, I would probably run it.