Why initial system-environment correlations do not imply the failure of complete positivity: a causal perspective

Abstract

When a system interacts with an environment with which it is initially uncorrelated, its evolution is described by a completely positive map.  The common wisdom in the field of quantum information theory, however, is that when the system is initially correlated with the environment, the map describing its evolution may fail to be completely positive. This has motivated many researchers to try and characterize this putatively more general sort of dynamics, and even the textbook of Nielsen and Chuang suggests that "It is an interesting problem for further research to study quantum information processing beyond the quantum operations formalism."  This talk will demonstrate that this common wisdom is mistaken.  The error can be traced to the standard argument for how the evolution map ought to be defined in such circumstances.  One can show that anomolous dynamics would arise even in completely classical examples if one were to follow the prescription of the standard argument.  The framework of classical causal models specifies how dynamics ought to be defined in such circumstances, and

the quantum analogue of this framework provides the correct definition of the quantum evolution map, which is found to be always completely positive.

Joint work with David Schmid