# New Minkowski type inequalities and entropic inequalities for quantum states of qudits

@article{Manko2014NewMT,
title={New Minkowski type inequalities and entropic inequalities for quantum states of qudits},
author={Vladimir I. Man'ko and L. A. Markovich},
journal={International Journal of Quantum Information},
year={2014},
volume={12},
pages={1560021}
}
• Published 1 September 2014
• Mathematics
• International Journal of Quantum Information
The two-parameter Minkowski like inequality written for composite quantum system state is obtained for arbitrary Hermitian non-negative matrix with trace equal to unity. The inequality can be used as entropic and information inequality for density matrix of noncomposite finite quantum system, e.g. for a single qudit state. The analogs of strong subadditivity condition for the single qudit is discussed in context of obtained Minkowski like inequality.
5 Citations

## Figures from this paper

Deformed Subadditivity Condition for Qudit States and Hybrid Positive Maps
• Mathematics
• 2014
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
Inequalities for Purity Parameters of Multiqudit and Single-Qudit States
• Mathematics
• 2016
We analyze the recently found inequality for eigenvalues of the density matrix and purity parameters describing either a bipartite-system state or a single-qudit state. We rewrite the Minkowski-type
Inequalities for purity parameters for multipartite and single qudit states
• Physics
• 2015
We analyze a recently found inequality for eigenvalues of the density matrix and purity parameter describing either a bipartite system state or a single qudit state. The Minkowski type trace
Properties of Nonnegative Hermitian Matrices and New Entropic Inequalities for Noncomposite Quantum Systems
• Physics
Entropy
• 2015
This work considers the probability distributions, spin (qudit)-state tomograms and density matrices of quantum states, and their information characteristics, 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.
No-Signaling Property of the Single-Qudit-State Tomogram
• Physics
• 2014
We review the tomographic approach to the description of quantum states of photons and qudits. We show that the no-signaling property exists for both tomograms of two-mode states of photons and

## References

SHOWING 1-10 OF 21 REFERENCES
Subadditivity Condition for Spin Tomograms and Density Matrices of Arbitrary Composite and Noncomposite Qudit Systems
• Physics
• 2014
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
The quantum strong subadditivity condition for systems without subsystems
• Physics
• 2014
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
New Inequality for Density Matrices of Single Qudit States
• Physics
• 2014
Using the monotonicity of relative entropy of composite quantum systems, we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Examples of qutrit state
Generalized Qubit Portrait of the Qutrit-State Density Matrix
• Mathematics
• 2013
We obtain new inequalities for tomographic probability distributions and density matrices of qutrit states by generalization of the qubit-portrait method. We propose an approach based on the
Tomographic and Improved Subadditivity Conditions for Two Qubits and a Qudit with j = 3/2
• Physics
• 2014
We obtain a new entropic inequality for quantum and tomographic Shannon information for systems of two qubits. We derive the inequality relating quantum information and spin-tomographic information
Separability and Entanglement of the Qudit X-State with j = 3/2
• Physics
• 2014
We study the qudit state with spin j = 3/2 and the density matrix of the form corresponding to the X state of two qubits and consider the entanglement and separability properties. We use the qubit
New Inequalities for Quantum Von Neumann and Tomographic Mutual Information
• Physics
• 2014
We study the entropic inequalities related to the quantum mutual information for bipartite system and tomographic mutual information for the Werner state of two qubits. We discuss quantum
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model.
• Werner
• Physics
Physical review. A, General physics
• 1989
Any classically correlated state can be modeled by a hidden-variable theory and hence satisfies all generalized Bell's inequalities and the converse of this statement is false.
A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy
• Mathematics
• 2002
We consider the following trace function on n-tuples of positive operators: $${\Phi _P}({A_1},{A_2},...,{A_n}) = Tr({(\sum\limits_{j = 1}^n {A_j^P} )^{1/P}})$$ and prove that it is jointly
Spin state tomography
• Physics, Mathematics
• 1997
A scheme for measuring the quantum state for an arbitrary spin is proposed that is analogous to the symplectic tomography scheme used to measure quantum states associated with continuous observables