Re: [asa] Information and knowledge

You can say that again. On the other hand, the issues of the relationship between genetic coding and information theory probably doesn't hang on a quantum vs a classical system. Most of the macroscopic systems don't have entangled particles with a lot of coherence.

Qubits are indeed fascinating. We studied quantum information theory a lot, especially as it related to quantum computing. As I think I've stated previously, we achieved one of the noteworthy milestones in our lab about 7 years ago. We hired Isaac Chang from MIT to come and build a quantum computer based on NMR. He actually succeeded and used a 7 qubit system to demonstrate that the factors of 15 were 3 and 5. At least it worked but it isn't scalable so the race is on for a different approach.

Randy
  Rich wrote:

  We need to bring in quantum information theory. Shannon's noisy coding theorem notes that the bandwidth of a channel decreases with noise. In the quantum variant, the bandwidth of a channel may increase with noise! It also means that quantum information can be negative! Take away point. Information theory is not necessarily intuitive.

  Reference: http://arxiv.org/abs/quant-ph/0505062

    Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned on it's prior information. It turns out to be given by an extremely simple formula, the conditional entropy. In the classical case, partial information must always be positive, but we find that in the quantum world this physical quantity can be negative. If the partial information is positive, its sender needs to communicate this number of quantum bits to the receiver; if it is negative, the sender and receiver instead gain the corresponding potential for future quantum communication. We introduce a primitive "quantum state merging" which optimally transfers partial information. We show how it enables a systematic understanding of quantum network theory, and discuss several important applications including distributed compression, multiple access channels and multipartite assisted entanglement distillation (localizable entanglement). Negative channel capacities also receive a natural interpretation.

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Received on Wed Apr 11 21:04:07 2007