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