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

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

References

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