Department of Physics & Astronomy Faculty of Science, Macquarie University, Australia
One of the best signatures of nonclassicality in a quantum system is the existence of correlations that have no classical counterpart. Different methods for quantifying the quantum and classical parts of the correlations are amongst the most actively-studied topics of quantum information theory in the past decade. Entanglement is the most prominent of these correlations, but in many cases unentangled states exhibit nonclassi-cal behavior. Thus distinguishing quantum correlation other than entanglement provides a better division between the quantum and classical worlds, especially when considering mixed states. Here we review different notions of classical and quantum correlations quantified by quantum discord and other related measures. In the first half we review the mathematical properties of the measures of quantum correlation, relate them to each other, and discuss the classical-quantum division that is common among them. In the second half, we show that the measures quantum correlation identify and quantify the deviation from classicality in various quantum information-processing tasks, quan-tum thermodynamics, open-system dynamics, and many-body physics. We show that in many cases quantum correlations indicate an advantage of quantum methods over classical ones.
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"The two-qubit systems can demonstrate quantum correlations and these correlations correspond to entanglement phenomenon  or to the violation of Bell inequalities . Also the correlations can be associated with quantum discord  . The quantum discord is related to difference of classical Shannon information behavior  and quantum information behavior determined by von Neumann entropy of a composite bipartite systems and the entropies of its subsystems. "
[Show abstract][Hide abstract] ABSTRACT: Entropic inequalities related to the quantum mutual information for bipartite
system and tomographic mutual information is studied for Werner state of two
qubits. Quantum correlations corresponding to entanglement properties of the
qubits in Werner state are discussed.
Full-text · Article · Mar 2014 · Journal of Russian Laser Research
"Several measures of entanglement have been introduced in the literature with the aim of characterizing quantum correlations and its usefulness in specific applications -. Starting with the entanglement of formation, most of these measures point to the quantification of the entanglement content of a given state. A different approach to this general problem has been proposed in  : the idea is to obtain information about the magnitude of non-classical correlations contained in a state ρ by studying how much it can be mixed with other states before becoming separable. "
[Show abstract][Hide abstract] ABSTRACT: The robustness properties of bipartite entanglement in systems of N bosons
distributed in M different modes are analyzed using a definition of
separability based on commuting algebras of observables, a natural choice when
dealing with identical particles. Within this framework, expressions for the
robustness and generalized robustness of entanglement can be explicitly given
for large classes of boson states: their entanglement content results in
general much more stable than that of distinguishable particles states. Using
these results, the geometrical structure of the space of N boson states can be
Full-text · Article · Apr 2012 · Physical Review A
"It is worth emphasizing: quantum correlations relativity is not a consequence of the reference-frame change or of the more general relativistic considerations such as e.g. in  . The degrees-of-freedom transformations implicit to our considerations cannot be written in a separable form for the unitary operators, i.e. in the form U 1 ⊗ U 2 for the 1 + 2 structure–such transformations are known to preserve discord    (and the references therein). Interestingly enough, some formally trivial variables transformations exhibit QCR also for the finite-dimensional (e.g. "