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Triangle Geometry for Qutrit States in the Probability Representation

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

arXiv:1804.04886Journal of Russian Laser ResearchSep 1, 201735 citations

Triangle Geometry of Spin States and Nonlinear Superposition of Probabilities Describing These States†

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

Journal of Russian Laser ResearchJan 1, 20195 citations

Quantum suprematism picture of Triada of Malevich’s squares for spin states and the parametric oscillator evolution in the probability representation of quantum mechanics

V. N. Chernega, O. V. Man’ko, V. 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 entropy–information inequalities are obtained for Franck–Condon factors. Density matrices of qudit states are expressed in terms of probabilities of artificial qubits as well as the quantum suprematism approach to geometry of these states using the triadas of Malevich squares is developed. Examples of qubits, qutrits and ququarts are considered.Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin–systems with discrete variables. New entropy–information inequalities are obtained for Franck–Condon factors. Density matrices of qudit states are expressed in terms of probabilities of artificial qubits as well as the quantum suprematism approach to geometry of these states using the triadas of Malevich squares is developed. Examples of qubits, qutrits and ququarts are considered.

arXiv:1712.01927Journal of Physics Conference SeriesAug 1, 201817 citations

Qubits and two-level atom states in representation of Malevich's squares

Vladimir N. Chernega, Olga V. Man’ko

New description of two-level atom states as well as spin-1/2 states by means of standard probability distribution is constructed. It is used as alternative of wave functions and density operators. The quantum suprematism picture of the states in terms of Malevich's squares triada is presented.

EPJ Web of ConferencesJan 1, 20191 citation

Geometry of the state spaces in quantum probability

Sh. A. Ayupov, N. J. Yadgorov

De Gruyter eBooksDec 31, 19940 citations

Geometry and Entanglement of Two-Qubit States in the Quantum Probabilistic Representation

Julio A. López-Saldívar, Octavio Castaños, Eduardo Nahmad-Achar +3 more

A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres-Horodecki positive partial transpose (ppt) -criterion and the concurrence inequalities are formulated as the conditions that the introduced probability distributions must satisfy to present entanglement. A four-level system, where one or two states are inaccessible, is considered as an example of applying the elaborated probability approach in an explicit form. The areas of three Triadas of Malevich's squares for entangled states of two qubits are defined through the qutrit state, and the critical values of the sum of their areas are calculated. We always find an interval for the sum of the square areas, which provides the possibility for an experimental checkup of the entanglement of the system in terms of the probabilities.A new geometric representation of qubit and qutrit states based on probability simplexes is used to describe the separability and entanglement properties of density matrices of two qubits. The Peres-Horodecki positive partial transpose (ppt) -criterion and the concurrence inequalities are formulated as the conditions that the introduced probability distributions must satisfy to present entanglement. A four-level system, where one or two states are inaccessible, is considered as an example of applying the elaborated probability approach in an explicit form. The areas of three Triadas of Malevich's squares for entangled states of two qubits are defined through the qutrit state, and the critical values of the sum of their areas are calculated. We always find an interval for the sum of the square areas, which provides the possibility for an experimental checkup of the entanglement of the system in terms of the probabilities.

arXiv:1808.08194EntropyAug 24, 201833 citations

Triangle Geometry of the Qubit State in the Probability Representation Expressed in Terms of the Triada of Malevich’s Squares

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Triangle Geometry of the Qubit State in the Probability Representation Expressed in Terms of the Triada of Malevich’s Squares

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