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Journal of Physics Conference Series

Hidden correlations in quantum optics and quantum information

Margarita A. Man’ko

Published Aug 1, 2018• 4 citations
Publisher

Abstract

We review the notion of quantum correlations in composite systems and show that noncomposite systems have similar correlations (which we call "hidden" correlations); these quantum correlations are analogous to the ones available in composite (multipartite) systems. We demonstrate new entropic-information inequalities characterizing the hidden correlations in noncomposite systems and present the examples of some qudit states with such correlations.

DOI
10.1088/1742-6596/1071/1/012015

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We review the notion of quantum correlations in composite systems and show that noncomposite systems have similar correlations (which we call "hidden" correlations); these quantum correlations are analogous to the ones available in composite (multipartite) systems. We demonstrate new entropic-information inequalities characterizing the hidden correlations in noncomposite systems and present the examples of some qudit states with such correlations.
For noncomposite systems in classical and quantum domains, we obtain new inequalities such as the subadditivity and strong subadditivity conditions for Shannon entropies and information determined by the probability distributions and for von Neumann entropies of quantum states determined by the density operators. We extend the relations of Shannon and Tsallis entropies to the entropies of conditional probability distributions known for composite systems to the case of noncomposite systems. We give a review of the approach to construct the tomographic-probability distributions for qudit systems and present the entropic and information inequalities for spin tomograms, as well as the subadditivity and strong subadditivity conditions for tomograms of the both noncomposite and composite system states.
We discuss the notion of hidden correlations in classical and quantum indivisible systems along with such characteristics of the correlations as the mutual information and conditional information corresponding to the entropic subadditivity condition and the entropic strong subadditivity condition. We present an analog of the Bayes formula for systems without subsystems, study entropic inequality for von Neumann entropy and Tsallis entropy of the single-qudit state, and discuss the inequalities for qubit and qutrit states as an example.
We show that the density-matrix states of noncomposite qudit systems satisfy entropic and information relations like the subadditivity condition, strong subadditivity condition, and Araki-Lieb inequality, which characterize hidden quantum correlations of observables associated with these indivisible systems. We derive these relations employing a specific map of the entropic inequalities known for density matrices of multiqudit systems to the inequalities for density matrices of single-qudit systems. We present the obtained relations in the form of mathematical inequalities for arbitrary Hermitian N × N -matrices. We consider examples of superconducting qubits and qudits. We discuss the hidden correlations in single- qudit states as a new resource for quantum technologies analogous to the known resource in correlations associated with the entanglement in multiqudit systems.
Abstract We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we study the bipartite case and the connection of two typically applied and distinctively different concepts of nonclassicality in quantum optics and quantum information. Our investigation includes the representation of correlated states in terms of quasiprobability matrices, a comparative study of joint and conditional quantum correlations, and an entanglement characterization. It is, for example, shown that our composition approach always includes entanglement as one form of quantum correlations. Yet, other forms of quantum correlations can also occur without entanglement. Finally, we give an outlook towards multimode systems and temporal correlations.
Abstract We present a review of the general approach to the problem of correlations in classical statistics and quantum statistics of systems with different numbers of subsystems and demonstrate the information-entropic relations for systems without subsystems recently obtained for Shannon entropies. We present the example of a single-qudit state corresponding to the N-level atom, consider explicitly the qutrit state, and show that qutrit can be interpreted as a set of several qubits. For each of these qubits, there exist corresponding von Neumann entropies, and constraints for these entropies determine the hidden correlations between the qubits in spite of the fact that the qutrit does not contain any subsystem. These constraints are expressed in terms of nonnegativity of the mutual information introduced, which usually exists only for the states of systems with subsystems. The value of information parameterizes the hidden correlations of artificial qubits in the system. We discuss examples of some qudits.