![]() Conservation of randomness and information has been proven to hold over unitary transforms and partial traces. More specifically, given density matrices ρ and σ, is it always the case that I ( ρ : ρ ) > + I ( ρ : σ )? Is it true that every quantum state is typical of μ? For all density matrices ρ, is it the case that d ( ρ | μ ) = O ( 1 )? Since d ( ρ | μ ) 2 < + I ( ρ : ρ ), we have that d ( ρ | μ ) < + √ 2 n. One question is whether a quantum state has maximized information with itself. ![]() ![]() There are still many open problems with respect to algorithmic quantum deficiency of randomness and information.
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