Entropy exchange explained

\phi acting on the density matrix \rho _{Q} of a system Q is defined asS(\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| , Tr _{R[\rho} _{QR} ] = \rho _{Q} , and\rho _{QR} ' = (\phi _{Q} ⊗ 1 _{R} )[\rho _{QR} ] , where in the above equation (\phi _{Q} ⊗ 1 _{R} ) acts on Q leaving R unchanged.

References

• Book: Nielsen. Michael Nielsen. Chuang. Isaac L.. Isaac Chuang. Quantum Computation and Quantum Information. Cambridge University Press. Cambridge. 2010. 2nd. 844974180. 978-1-107-00217-3.