Publication details

Divisibility of qubit channels and dynamical maps

Authors

DAVALOS David ZIMAN Mário PINEDA Carlos

Year of publication 2019
Type Article in Periodical
Magazine / Source QUANTUM
MU Faculty or unit

Faculty of Informatics

Citation
Web http://dx.doi.org/10.22331/q-2019-05-20-144
Doi http://dx.doi.org/10.22331/q-2019-05-20-144
Keywords quantum channels; open system dynamics
Attached files
Description The concept of divisibility of dynamical maps is used to introduce an analogous concept for quantum channels by analyzing the simulability of channels by means of dynamical maps. In particular, this is addressed for Lindblad divisible, completely positive divisible and positive divisible dynamical maps. The corresponding L-divisible, CP-divisible and P-divisible subsets of channels are characterized (exploiting the results by Wolf et al. [25]) and visualized for the case of qubit channels. We discuss the general inclusions among divisibility sets and show several equivalences for qubit channels. To this end we study the conditions of L-divisibility for finite dimensional channels, especially the cases with negative eigen-values, extending and completing the results of Ref. [26]. Furthermore we show that transitions between every two of the defined divisibility sets are allowed. We explore particular examples of dynamical maps to compare these concepts. Finally, we show that every divisible but not infinitesimal divisible qubit channel (in positive maps) is entanglement-breaking, and open the question if something similar occurs for higher dimensions.
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