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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Holevo Quantity with Channel

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**