Abstract
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme.
Highlights
The ever-increasing processing power of current classical computers depends upon the corresponding increase in the capability of miniaturization of electronic components
For future purposes it is worth bearing in mind that the notion of quantum discord to quantify total quantum correlations is implicitly embedded into a theoretical framework where total correlations are additive, i.e., they are given by the addition of classical and quantum correlations
We used squared Bures and squared Hellinger distances, in addition to quantum Jensen–Shannon divergence, to define measures of total, classical and quantum correlations. We applied these measures to analyze the behavior of correlations under non-dissipative decoherence in two-qubit states with maximally mixed marginals in different dynamical scenarios of physical relevance
Summary
The ever-increasing processing power of current classical computers depends upon the corresponding increase in the capability of miniaturization of electronic components. A number of theoretical and experimental results points to an increment in efficiency due to the existence of correlations of a different nature that entanglement [3,4,5,6,7,8,9,10]. Another aspect to be considered in tasks of Quantum information processing and quantum computing is the fact that quantum correlations are very sensitive to uncontrolled interactions between the system and its environment.
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