Quantum Bayesian Networks

May 14, 2011

SIT-ting without the Deltas and Epsilons

Filed under: Uncategorized — rrtucci @ 7:59 pm

Lately, I’ve been very busy working on Shannon Information Theory (SIT). I previously wrote the following blog posts about quantum SIT

Quantum SIT has advanced by leaps and bounds in the last two decades, but I believe many aspects of it could still stand some improvements and enhancements. For example: for my taste, current treatments of quantum SIT use too many delta and epsilon arguments; they seem to me to be too epsilon and delta “trigger happy”. The situation reminds me of Calculus, where delta and epsilon arguments are useful if one wants to achieve a very high level of rigor, but can be avoided for the most part if one doesn’t mind being slightly unrigorous.

I’ve invented a new SIT technique that doesn’t use deltas and epsilons at all, or does so very sparingly. My technique is not as rigorous as the standard delta & epsilon techniques used in SIT, in the same way that an engineering Calculus book is not as rigorous as Rudin’s analysis book. However, my technique has the virtue that it makes proofs much more automatic and briefer. One could say that I am translating SIT from the language of pure mathematicians to a language that physicists might find more palatable. Using my new technique, I can easily prove the two main pillars of classical SIT: the noiseless coding theorem and the noisy channel coding theorem. Using a quantum generalization of my new technique, I am now trying to re-derive the most important already known results in quantum SIT for noiseless and noisy coding.

At the risk of pulling a Fermat’s Last Theorem trick on the readers of this blog, I promise to unveil my new results at a later time (assuming that I don’t eventually find a fatal flaw in my technique, and assuming that I eventually derive some nontrivial, previously unknown results in quantum SIT).

P.S. On my next blog post, I’ll say something about D-Wave’s exciting new results. These days, there is certainly no shortage of interesting quantum computing topics to write blog posts about.

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2 Comments »

  1. I believe that Devetak, Harrow, and Winter were trying to do something along these lines in the following paper:

    http://arxiv.org/abs/quant-ph/0512015

    Comment by Mark Wilde — May 27, 2011 @ 12:39 am

  2. Yes. I agree. I’m doing something slightly different. But I hope my puny ideas will intersect theirs at some point.

    Comment by rrtucci — May 27, 2011 @ 12:54 am


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