Searcharxiv⌕ Search

arXiv subjects

V. N. Chernega

Publications and source records attributed to V. N. Chernega.

15 recordsLinked to original sources
arXiv2019

Probability representation of quantum mechanics and star product quantization

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 obtained by means of bijective maps of the operators acting in Hilbert space onto these functions is presented. Examples of the Wigner-Weyl symbols (like Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified with the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators which are needed to construct the bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relation of the structure constants of the associative star-product of the operator symbols to the quantizer-dequantizer operators is reviewed.

quant-ph↗
arXiv2017

New information and entropic inequalities for Clebsch-Gordan coefficients

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 associated with the Wigner 3-j symbols are obtained using the relation of Clebsch-Gordan coefficients with probability distributions interpreted either as distributions for composite systems or distributions for noncomposite systems. The new inequalities were found for Hahn polynomials and hypergeometric functions

quant-ph↗
arXiv2015

No signaling and strong subadditivity condition for tomographic q-entropy of single qudit states

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 the composite and noncomposite systems characterizing correlations in these systems are discussed. The spin tomographic probability distributions determining the single qudit states are demonstrated to satisfy the strong subadditivity condition for Tsallis q-entropy. Examples of the new entropic inequalities for q-entropy are considered for qudits with j = 5=2, j = 7=2.

quant-ph↗
arXiv2014

New inequality for density matrices of single qudit states

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 state inequalities and the "qubit portrait" bound for the distance between the qutrit states are considered in explicit form.

quant-ph↗
arXiv2014

Density matrix form of Gross-Pitaevskii equation

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 matrix corresponds to the solutions of Gross-Pitaevskii equation.

quant-ph↗
arXiv2014

Subadditivity condition for spin-tomograms and density matrices of arbitrary composite and noncomposite qudit systems

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 coincides with this subadditivity condition for the system of two qudits. The general statement on existence of the subadditivity condition for arbitrary probability distribution and arbitrary qudit-system tomogram is formulated. The nonlinear quantum channels creating the entangled states from separable ones are discussed.

quant-ph↗
arXiv2014

Tomographic and improved subadditivity conditions for two qubits and qudit with j = 3=2

New entropic inequality for quantum and tomographic Shannon information for system of two qubits is obtained. The inequality relating quantum information and spin-tomographic information for particle with spin j = 3=2 is found. The method to extend the obtained new entropic and information inequalities for one qudit and arbitrary composite system of qudits is suggested.

quant-ph↗
arXiv2013

Generalized qubit portrait of the qutrit state density matrix

New inequalities for tomographic probability distributions and density matrices of qutrit states are obtained by means of generalization of qubit portrait method. The approach based on the qudit portrait method to get new entropic inequalities is proposed. It can be applied to the case of arbutrary nonnegative hermitian matrices including the density matrices of multipartite qudit states.

quant-ph↗
arXiv2013

Purity dependent uncertainty relation and possible enhancement of quantum tunneling phenomenon

The position-momentum uncertainty relations containing the dependence of their quantum bounds on state purity parameter $μ$ are discussed in context of possibilities to influence on the potential barrier transparency by means of decoherence processes. The behavior of barrier transparency $D$ is shown to satisfy the condition $μ^{-1}\ln D=const$. The particular case of thermal state with temperature $T$ where the purity parameter is a function of temperature is considered. For large temperature the condition for the barrier transparency is shown to be $T\ln D=const$.

quant-ph↗
arXiv2012

State-extended uncertainly relations and tomographic inequalities as quantum system state characteristics

Some inequalities for probability vector are discussed. The probability representation of quantum mechanics where the states are mapped onto probability vectors (either finite or infinite dimensional) called the state tomograms is used. Examples of inequalities for qudit tomograms and a state extended uncertainly relation are considered. Tomographic cumulant related to photon state tomographic probability distributions is introduced and it is used as parameter of the state nongaussianity.

quant-ph↗
arXiv2011

Probability representation and state-extended uncertainty relations

The new inequality recently found by Trifonov and called the state-extended inequality is considered in the tomographic-probability representation of quantum mechanics. The Trifonov uncertainty relations are expressed in terms of optical tomograms and can be checked in experiments on homodyne detection of the photon states.

quant-ph↗
arXiv2009

Radon transform and kinetic equations in tomographic representation

Statistical properties of classical random process are considered in tomographic representation. The Radon integral transform is used to construct the tomographic form of kinetic equations. Relation of probability density on phase space for classical systems with tomographic probability distributions is elucidated. Examples of simple kinetic equations like Liouville equations for one and many particles are studied in detail.

quant-ph↗
arXiv2006

Qubit portrait of qudit states and Bell inequalities

A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. Using the qubit portrait method the Bell inequalities for two qubits and two qutrits are discussed in framework of probability representation of quantum mechanics. Semigroup of stochastic matrices is associated with tomographic probability distributions of qubit and qutrit states. Bell-like inequalities are studied using the semigroup of stochastic matrices. The qudit-qubit map of tomographic probability distributions is discussed as ansatz to provide a necessary condition for separability of quantum states.

quant-ph↗