48 citations · 324 across the 25 of their papers we have counts for
26 papers
Entangled probability distributions
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
Concept of entangled probability distribution of several random variables is introduced. These probability distributions describe multimode quantum states in probability representa…
Coherent states of parametric oscillators in the probability representation of quantum mechanics
Vladimir N. Chernega, Olga V. Man'ko
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states…
Spin kinetic equations in the probability representation of quantum mechanics
Vladimir N. Chernega, Vladimir I. Man'ko
We discuss the possibility to formulate the dynamics of spin states described by the Schrodinger equation for pure states and the von Neumann equation (as well as the GKSL equatio…
Probability representation of photon states and tomography
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of stand…
Probability representation of quantum states as a renaissance of hidden variables -- God plays coins
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
We develop an approach where the quantum system states and quantum observables are described as in classical statistical mechanics -- the states are identified with probability dis…
Probability representation of quantum mechanics and star product quantization
S. N. Belolipetskiy, V. N. Chernega, O. V. Man'ko +1
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are ob…
Correlations in a system of classical--like coins simulating spin-1/2 states in the probability representation of quantum mechanics
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
An analog of classical "hidden variables" for qubit states is presented. The states of qubit (two-level atom, spin-1/2 particle) are mapped onto the states of three classical--like…
Damped Oscillator with delta-kicked frequency in probability representation of quantum mechanic
Vladimir N. Chernega, Olga V. Man'ko
We obtain the tomogram of squeezed correlated states of a quantum parametric damped oscillator in an explicit form. We study the damping within the framework of the Caldirola--Kana…
Probability representation of quantum observable and quantum states
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions…
Triangle geometry for qutrit states in the probability representation
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
We express the matrix elements of the density matrix of the qutrit state in terms of probabilities associated with artificial qubit states. We show that the quantum statistics of q…
Triangle geometry of the qubit state in the probability representation expressed in terms of the triada of Malevich's Squares
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
We map the density matrix of the qubit (spin-1/2) state associated with the Bloch sphere and given in the tomographic probability representation onto vertices of a triangle determi…
God plays coins or superposition principle for classical probabilities in quantum suprematism representation of qubit states
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
For three given probability distributions describing positions of three classical coins the quantum density matrix of spin- state is constructed and its matrix elements are as…
Quantum suprematism picture of Malevich's squares triada for spin states and the parametric oscillator evolution in the probability representation of quantum mechanics
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New…
New information and entropic inequalities for Clebsch-Gordan coefficients
V. N. Chernega, O. V. Manko, V. I. Manko +1
The Clebsch-Gordan coefficients of the group SU(2) are shown to satisfy new inequalities. They are obtained using the properties of Shannon and Tsallis entropies. The inequalities…
No signaling and strong subadditivity condition for tomographic q-entropy of single qudit states
V. N. Chernega, O. V. Man'ko
The single qudit state tomograms are shown to have the no signaling property. The known and new entropic and information inequalities for Shannon, von Neumann and q-entropies of th…
Deformed entropy and information relations for composite and noncomposite systems
Vladimir N. Chernega, Olga V. Man'ko, Vladimir I. Man'ko
The notion of conditional entropy is extended to noncomposite systems. The q-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees…
New inequality for density matrices of single qudit states
V. N. Chernega, O. V. Man'ko, V. I. Man'ko
Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit s…
Minkovskii-type inequality for arbitrary density matrix of composite and noncomposite systems
V. N. Chernega, O. V. Man'ko, V. I. Man'ko
New kind of matrix inequality known for bipartite system density matrix is obtained for arbitrary density matrix of composite or noncomposite qudit systems including the single qud…
Density matrix form of Gross-Pitaevskii equation
V. N. Chernega, O. V. Man'ko, V. I. Man'ko
We consider the generalized pure state density matrix which depends on different time moments. The evolution equation for this density matrix is obtained in case where the density…
Subadditivity condition for spin-tomograms and density matrices of arbitrary composite and noncomposite qudit systems
V. N. Chernega, O. V. Man'ko, V. I. Man'ko
New quantum entropic inequality for states of system of n >_ 1 qudits is obtained. The inequality has the form of quantum subadditivity condition of bipartite qudit system and coin…
Tomographic and improved subadditivity conditions for two qubits and qudit with j = 3=2
V. N. Chernega, O. V. Man'ko
New entropic inequality for quantum and tomographic Shannon information for system of two qubits is obtained. The inequality relating quantum information and spin-tomographic infor…
Generalized qubit portrait of the qutrit state density matrix
V. N. Chernega, O. V. Man'ko, V. I. Man'ko
New inequalities for tomographic probability distributions and density matrices of qutrit states are obtained by means of generalization of qubit portrait method. The approach base…
Purity dependent uncertainty relation and possible enhancement of quantum tunneling phenomenon
V. N. Chernega
The position-momentum uncertainty relations containing the dependence of their quantum bounds on state purity parameter are discussed in context of possibilities to influence o…
State-extended uncertainly relations and tomographic inequalities as quantum system state characteristics
V. N. Chernega, V. I. Man'ko
Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or i…