Entropy exchange

In quantum mechanics, and especially quantum information processing, the entropy exchange of a quantum operation $\phi \,$ acting on the density matrix $\rho _{Q}\,$ of a system $Q\,$ is defined as

S(\rho ,\phi )\equiv S[Q',R']=S(\rho _{QR}')

where $S(\rho _{QR}')\,$ is the von Neumann entropy of the system $Q\,$ and a fictitious purifying auxiliary system $R\,$ after they are operated on by $\phi \,$ . Here,

\rho _{QR}=|QR\rangle \langle QR|\quad ,

\mathrm {Tr} _{R}[\rho _{QR}]=\rho _{Q}\quad ,

and

\rho _{QR}'=\phi [\rho _{QR}]\quad ,

where in the above equation $\phi$ acts on $Q$ leaving $R$ unchanged.

References

Nielsen, Michael A. and Isaac L. Chuang (2000). Quantum Computation and Quantum Information, Cambridge University Press, ISBN 0-521-63503-9

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