The Experts below are selected from a list of 4323 Experts worldwide ranked by ideXlab platform
Andreas Winter - One of the best experts on this subject based on the ideXlab platform.
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A New Inequality for the von Neumann Entropy
Communications in Mathematical Physics, 2005Co-Authors: Noah Linden, Andreas WinterAbstract:Strong Subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of strong Subadditivity: it is an inequality which is true for any four party quantum state, provided that it satisfies three linear relations (constraints) on the entropies of certain reduced states.
V I Manko - One of the best experts on this subject based on the ideXlab platform.
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deformed Subadditivity condition for qudit states and hybrid positive maps
Journal of Russian Laser Research, 2014Co-Authors: Margarita A Manko, V I MankoAbstract:We extend the Subadditivity condition for q-deformed entropy of a bipartite quantum system to the case of an arbitrary quantum system including the single qudit state. We present the Subadditivity condition for the density matrix of the single qutrit state in an explicit form. We obtain the inequality for the purity parameters of a bipartite quantum system and its subsystems. We propose a positive map construction using the fiducial density matrix.
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Subadditivity condition for spin tomograms and density matrices of arbitrary composite and noncomposite qudit systems
Journal of Russian Laser Research, 2014Co-Authors: Vladimir N Chernega, O V Manko, V I MankoAbstract:We obtain a new quantum entropic inequality for the states of a system of n ≥ 1 qudits. The inequality has the form of the quantum Subadditivity condition of a bipartite qudit system and coincides with the Subadditivity condition for the system of two qudits. We formulate a general statement on the existence of the Subadditivity condition for an arbitrary probability distribution and an arbitrary qudit-system tomogram. We discuss the nonlinear quantum channels creating the entangled states from separable states.
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the quantum strong Subadditivity condition for systems without subsystems
Physica Scripta, 2014Co-Authors: Margarita A Manko, V I MankoAbstract:The strong Subadditivity condition for the density matrix of a quantum system, which does not contain subsystems, is derived using the qudit-portrait method. An example of the qudit state in the seven-dimensional Hilbert space corresponding to spin j = 3 is presented in detail. New entropic inequalities in the form of the Subadditivity condition and strong Subadditivity condition for spin tomograms determining the qudit states are obtained and given on the example of j = 2 and 3.
Karol życzkowski - One of the best experts on this subject based on the ideXlab platform.
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composition of quantum states and dynamical Subadditivity
Journal of Physics A, 2008Co-Authors: Wojciech Roga, Mark Fannes, Karol życzkowskiAbstract:We introduce a composition of quantum states of a bipartite system which is based on the reshuffling of density matrices. This non-Abelian product is associative and stems from the composition of quantum maps acting on a simple quantum system. It induces a semi-group in the subset of states with maximally mixed partial traces. Subadditivity of the von Neumann entropy with respect to this product is proved. It is equivalent to Subadditivity of the entropy of bistochastic maps with respect to their composition, where the entropy of a map is the entropy of the corresponding state under the Jamiolkowski isomorphism. Strong dynamical Subadditivity of a concatenation of three bistochastic maps is established. Analogous bounds for the entropy of a composition are derived for general stochastic maps. In the classical case they lead to new bounds for the entropy of a product of two stochastic matrices.
Margarita A. Man’ko - One of the best experts on this subject based on the ideXlab platform.
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Hidden Correlations and Entanglement in Single-Qudit States^†
Journal of Russian Laser Research, 2018Co-Authors: Margarita A. Man’ko, Vladimir I. Man’koAbstract: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.
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Entropic and Information Inequalities for Indivisible Qudit Systems^*
Journal of Russian Laser Research, 2016Co-Authors: Margarita A. Man’koAbstract:We present the idea that in both classical and quantum systems all correlations available for composite multipartite systems, e.g., bipartite systems, exist as “hidden correlations” in indivisible (noncomposite) systems. The presence of correlations is expressed by entropic-information inequalities known for composite systems like the Subadditivity condition. We show that the mathematically identical Subadditivity condition and the mutual information nonnegativity are available as well for noncomposite systems like a single-qudit state. We demonstrate an explicit form of the Subadditivity condition for a qudit with j = 2 or the five-level atom. We consider the possibility to check the Subadditivity condition (entropic inequality) in experiments where such a system is realized by the superconducting circuit based on Josephson-junction devices.
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Subadditivity and Strong Subadditivity Conditions for the Density Matrix of the Five-Level Atom
Journal of Russian Laser Research, 2016Co-Authors: Margarita A. Man’ko, Vladimir I. Man’koAbstract:We obtain new quantum inequalities for von Neumann entropy of the five-level atom, which are analogs of the Subadditivity condition known for bipartite quantum systems and the strong Subadditivity condition known for tripartite quantum systems. We discuss the possibility to check the inequalities for the single qudit with j = 2, which can be realized as a five-level atom in the experiments with superconducting circuits. We present the strong Subadditivity conditions for the finite-level atomic populations.
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Inequalities for nonnegative numbers and information properties of qudit tomograms
Journal of Russian Laser Research, 2013Co-Authors: Margarita A. Man’ko, Vladimir I. Man’koAbstract:We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the Subadditivity and strong Subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Rényi, and Tsallis entropies of spin states.
Vladimir I. Man’ko - One of the best experts on this subject based on the ideXlab platform.
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Hidden Correlations and Entanglement in Single-Qudit States^†
Journal of Russian Laser Research, 2018Co-Authors: Margarita A. Man’ko, Vladimir I. Man’koAbstract: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.
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Subadditivity and Strong Subadditivity Conditions for the Density Matrix of the Five-Level Atom
Journal of Russian Laser Research, 2016Co-Authors: Margarita A. Man’ko, Vladimir I. Man’koAbstract:We obtain new quantum inequalities for von Neumann entropy of the five-level atom, which are analogs of the Subadditivity condition known for bipartite quantum systems and the strong Subadditivity condition known for tripartite quantum systems. We discuss the possibility to check the inequalities for the single qudit with j = 2, which can be realized as a five-level atom in the experiments with superconducting circuits. We present the strong Subadditivity conditions for the finite-level atomic populations.
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Inequalities for nonnegative numbers and information properties of qudit tomograms
Journal of Russian Laser Research, 2013Co-Authors: Margarita A. Man’ko, Vladimir I. Man’koAbstract:We discuss some inequalities for N nonnegative numbers. We use these inequalities to obtain known inequalities for probability distributions and new entropic and information inequalities for quantum tomograms of qudit states. The inequalities characterize the degree of quantum correlations in addition to noncontextuality and quantum discord. We use the Subadditivity and strong Subadditivity conditions for qudit tomographic-probability distributions depending on the unitary-group parameters in order to derive new inequalities for Shannon, Rényi, and Tsallis entropies of spin states.
