Requiring linearity leads to complete positivity

Abstract

The reduced dynamics of an open quantum system $S$, interacting with its environment $E$, is not completely positive, in general. In this paper, we demonstrate that if the two following conditions are satisfied, simultaneously, then the reduced dynamics is completely positive: (1) the reduced dynamics of the system is linear, for arbitrary system-environment unitary evolution $U$; and (2) the reduced dynamics of the system is linear, for arbitrary initial state of the system ${\rho }_S$.

7 pages, 2 figures. The title is changed to match the published version

References in corpus (5)

• Vanishing quantum discord is necessary and sufficient for completely positive maps
• Completely Positive Maps and Classical Correlations
• Characterizing quantum dynamics with initial system-environment correlations
• Vanishing quantum discord is not necessary for completely-positive maps
• Completely positive maps within the framework of direct-sum decomposition of state space

Cited by in corpus (1)

• Limitations of the Markovian approximation in the harmonic oscillator