Entropy exchange - Alchetron, The Free Social Encyclopedia

In quantum mechanics, and especially quantum information processing, the entropy exchange of a quantum operation ϕ acting on the density matrix ρ Q of a system Q is defined as

S ( ρ , ϕ ) ≡ S [ Q ′ , R ′ ] = S ( ρ Q R ′ )

where S ( ρ Q R ′ ) is the von Neumann entropy of the system Q and a fictitious purifying auxiliary system R after they are operated on by ϕ . Here,

ρ Q R = | Q R ⟩ ⟨ Q R | , T r R [ ρ Q R ] = ρ Q ,

and

ρ Q R ′ = ϕ [ ρ Q R ] ,

where in the above equation ϕ acts on Q leaving R unchanged.

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