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Homework Help: Holevo Quantity with Channel

  1. Nov 17, 2011 #1
    I'm trying to prove that the Holevo quantity does not increase when a channel is applied to the ensemble of states.

    So, if

    [itex]\Phi[/itex](ε) = { (p(a), [itex]\Phi[/itex](ρa)) : a[itex]\in[/itex][itex]\Gamma[/itex]},

    then I want to prove that

    [itex]\chi[/itex]([itex]\Phi[/itex](ε)) ≤ [itex]\chi[/itex](ε)

    where [itex]\chi[/itex] refers to the Holevo quantity. I'm trying an approach similar to the proof for Holevo's theorem, but I can's say I totally understand that proof... but I don't think this should be too difficult. Please help!

    Thank you!
  2. jcsd
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