Quantum discord plays no distinguished role in characterization of complete positivity: Robustness of the traditional scheme

Abstract

The traditional scheme for realizing open-system quantum dynamics takes the initial state of the system-bath composite as a simple product. Currently, however, the issue of system-bath initial correlations possibly affecting the reduced dynamics of the system has been attracting considerable interest. The influential work of Shabani and Lidar [PRL {\bf 102}, 100402 (2009)] famously related this issue to quantum discord, a concept which has in recent years occupied the centre-stage of quantum information theory and has led to several fundamental results. They suggested that reduced dynamics is completely positive if and only if the initial system-bath correlations have vanishing quantum discord. Here we show that there is, within the Shabani-Lidar framework, no scope for any distinguished role for quantum discord in respect of complete positivity of reduced dynamics. Since most applications of quantum theory to real systems rests on the traditional scheme, its robustness demonstrated here could be of far-reaching significance.

5 pages, 1 figure. Minor typos corrected. Comments before submission of the manuscript to an appropriate journal will be greatly appreciated, particularly in view of the fact that our principal result seems to run counter to the position held by a large section of the recently published literature