Entropy exchange

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

S(ρ,ϕ)≡S[Q′,R′]=S(ρQ′R)

where S(ρQ′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,

ρQR=|QR⟩⟨QR|,
TrR[ρQR]=ρQ,

and

ρQ′R=ϕ[ρQR],

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

## References

* Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information (2nd ed.). Cambridge: Cambridge University Press. ISBN 978-1-107-00217-3. OCLC 844974180.

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