Nonlinear Constants of Quantum Information in Reversible and Irreversible Amplitude Flows

We report an approach to quantum open system dynamics that leads to novel nonlinear constant relations governing information flow among the participants. Our treatment is for mixed state systems entangled in a pure state fashion with an unspecified party that was involved in preparing the system for an experimental test, but no longer interacts after $t=0$. Evolution due to subsequent interaction with another party is treated as an amplitude flow channel and uses Schmidt-type bipartite decomposition of the evolving state. We illustrate this with three examples, including both reversible and irreversible information flows, and give formulas for the new nonlinear constraints in each case.