Remarks on ?On Completely Positive Maps in Generalized Quantum Dynamics?

Ralph F. Simmons, James L Park

Aharon Brodutch, Animesh Datta, Kavan Kishore Modi +2 more

The description of the dynamics of a system that may be correlated with its environment is only meaningful within the context of a specific framework. Different frameworks rely upon different assumptions about the initial system-environment state. We reexamine the connections between complete positivity and quantum discord within two different sets of assumptions about the relevant family of initial states. We present an example of a system-environment state with nonvanishing quantum discord that leads to a completely positive map. This invalidates an earlier claim about the necessity of vanishing quantum discord for completely positive maps. In our final remarks, we discuss the physical validity of each approach.

Paul Busch, PEKKA J. LAHTI

Longjiang Liu, D. M. Tong

We investigate completely positive maps for an open system interacting with its environment. The families of the initial states for which the reduced dynamics can be described by a completely positive map are identified within the framework of direct-sum decomposition of state space. They include not only separable states with vanishing or nonvanishing quantum discord but also entangled states. A general expression of the families as well as the Kraus operators for the completely positive maps are explicitly given. It significantly extends the previous results.

Fabio Benatti, Roberto Floreanini B, Marco Piani