Quantum correlations expressed as information and entropic inequalities for composite and noncomposite systems

Abstract

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.

14 pages, to be published in J. Phys. Conf. Ser. in the Proceedings of the XVI Symposium "Symmetries in Science" (Bregenz, Austria, July 21--26, 2013)

References in corpus (3)

• A simple test for hidden variables in spin-1 system
• A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity
• State-independent contextuality with identical particles

Cited by in corpus (3)

• Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits
• Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
• Information processing using three-qubit and qubit-qutrit encodings of noncomposite quantum systems