Completely positive maps and classical correlations

By César A. Rodríguez-Rosario, Kavan Modi, Aik-meng Kuah, Anil Shaji, E. Sudarshan. 2007

170 citations recorded by the source corpus.

We expand the set of initial states of a system and its environment that are known to guarantee completely positive reduced dynamics for the system when the combined state evolves unitarily. We characterize the correlations in the initial state in terms of its quantum discord [1]. We prove that initial states that have only classical correlations lead to completely positive reduced dynamics. The induced maps can be not completely positive when quantum correlations including, but not limited to, entanglement are present.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/737e9871fd1abcf014c01383744e06454f2505f3

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Dynamics of non-Markovian open quantum systems (2015, background): “In addition, was proven by Rodriguez-Rosario et al. (2008) that initial states with zero discord (Modi et al., 2012a; Ollivier and Zurek, 2001), such as (31), i.e. fulfilling the property [ρs(0) ⊗ 11B , ρtot(0)] = 0, lead to completely positive reduced dynamics.”
Observing the operational significance of discord consumption (2012, background): “Discord has thus captured a great deal of attention, as evidenced by studies of its role in open dynamics [15], cloning of correlations [16, 17], scaling laws in many-body physics [18], and quantum correlations within continuous variable systems [19, 20].”