Entropy exchange

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

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,

and

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