Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1406.5838 · Journal of Russian Laser Research

New Inequality for Density Matrices of Single Qudit States

Vladimir N. Chernega, Olga V. Man’ko, Vladimir I. Man’ko

Published Sep 1, 2014• 16 citations
arXivHTMLPDF
DOI
10.1007/s10946-014-9447-y

Related papers

Inequalities for Purity Parameters of Multiqudit and Single-Qudit States

Vladimir I. Man’ko, Liubov A. Markovich

Journal of Russian Laser Research•Mar 1, 2016•1 citation

The maps of matrices and portrait maps of density operators of composite and noncomposite systems

Margarita A. Man’ko, Vladimir I. Man’ko

We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by "portrait" map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and an discuss entangled single qudit state. We consider in detail the examples of N=3 and 4. Also we point out a possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations.

arXiv:1404.3650•Apr 14, 2014•2 citations

Local discrimination of qudit lattice states

Ying‐Hui Yang, Qianqian Liu, Guang-Wei Mi +1 more

Quantum Information Processing•Sep 17, 2022•3 citations

Hidden Correlations in Indivisible Qudits as a Resource for Quantum Technologies on Examples of Superconducting Circuits

Margarita A. Man’ko, Vladimir I. Man’ko

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.

arXiv:1512.08368•Journal of Physics Conference Series•Mar 1, 2016•5 citations

Properties of Nonnegative Hermitian Matrices and New Entropic Inequalities for Noncomposite Quantum Systems

Margarita A. Man’ko, Vladimir I. Man’ko

We consider the probability distributions, spin (qudit)-state tomograms and density matrices of quantum states, and their information characteristics, such as Shannon and von Neumann entropies and q-entropies, from the viewpoints of both well-known purely mathematical features of nonnegative numbers and nonnegative matrices and their physical characteristics, such as entanglement and other quantum correlation phenomena. We review entropic inequalities such as the Araki–Lieb inequality and the subadditivity and strong subadditivity conditions known for bipartite and tripartite systems, and recently obtained for single qudit states. We present explicit matrix forms of the known and some new entropic inequalities associated with quantum states of composite and noncomposite systems. We discuss the tomographic probability distributions of qudit states and demonstrate the inequalities for tomographic entropies of the qudit states. In addition, we mention a possibility to use the discussed information properties of single qudit states in quantum technologies based on multilevel atoms and quantum circuits produced of Josephson junctions.

Entropy•May 6, 2015•37 citations

Quantum States and the Density Matrix

WORLD SCIENTIFIC (EUROPE) eBooks•Nov 8, 2017•0 citations
We obtain a new inequality for arbitrary Hermitian matrices. We describe particular linear maps called the matrix portrait of arbitrary NxN matrices. The maps are obtained as analogs of partial tracing of density matrices of multipartite qudit systems. The structure of the maps is inspired by "portrait" map of the probability vectors corresponding to the action on the vectors by stochastic matrices containing either unity or zero matrix elements. We obtain new entropic inequalities for arbitrary qudit states including a single qudit and an discuss entangled single qudit state. We consider in detail the examples of N=3 and 4. Also we point out a possible use of entangled states of systems without subsystems (e.g., a single qudit) as a resource for quantum computations.
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.
We consider the probability distributions, spin (qudit)-state tomograms and density matrices of quantum states, and their information characteristics, such as Shannon and von Neumann entropies and q-entropies, from the viewpoints of both well-known purely mathematical features of nonnegative numbers and nonnegative matrices and their physical characteristics, such as entanglement and other quantum correlation phenomena. We review entropic inequalities such as the Araki–Lieb inequality and the subadditivity and strong subadditivity conditions known for bipartite and tripartite systems, and recently obtained for single qudit states. We present explicit matrix forms of the known and some new entropic inequalities associated with quantum states of composite and noncomposite systems. We discuss the tomographic probability distributions of qudit states and demonstrate the inequalities for tomographic entropies of the qudit states. In addition, we mention a possibility to use the discussed information properties of single qudit states in quantum technologies based on multilevel atoms and quantum circuits produced of Josephson junctions.