I'm trying to prove that the Holevo quantity does not increase when a channel is applied to the ensemble of states.(adsbygoogle = window.adsbygoogle || []).push({});

So, if

[itex]\Phi[/itex](ε) = { (p(a), [itex]\Phi[/itex](ρ_{a})) : 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!

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# Holevo Quantity with Channel

Can you offer guidance or do you also need help?

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