The positive vector optical tomogram fully describing the quantum state of spin 1/2 particle without any redundancy is introduced. Reciprocally the vector symplectic tomogram and vector quasidistributions $\vec W({\mathbf q},{\mathbf p})$ , $\vec Q({\mathbf q},{\mathbf p})$ , $\vec P(\vecα)$ are introduced. The evolution equations for proposed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are obtained. The quantum system of charged spin 1/2 particle in arbitrary electro-magnetic field is considered in proposed representations and evolution equations which are analogs of Pauli equation are obtained. The propagator of evolution equation in the case of homogeneous and stationary magnetic field in Landau gauge is found and the evolution of initial entangled superposition of lower Landau levels in the vector optical representation is considered. The system of linear quantum oscillator with spin in vector optical tomography representation is considered and the evolution of initial entangled superposition of two lower Fock states and spin-up, spin-down states is studied in this representation.The positive vector optical tomogram fully describing the quantum state of spin 1/2 particle without any redundancy is introduced. Reciprocally the vector symplectic tomogram and vector quasidistributions $\vec W({\mathbf q},{\mathbf p})$, $\vec Q({\mathbf q},{\mathbf p})$, $\vec P(\vecα)$ are introduced. The evolution equations for proposed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are obtained. The quantum system of charged spin 1/2 particle in arbitrary electro-magnetic field is considered in proposed representations and evolution equations which are analogs of Pauli equation are obtained. The propagator of evolution equation in the case of homogeneous and stationary magnetic field in Landau gauge is found and the evolution of initial entangled superposition of lower Landau levels in the vector optical representation is considered. The system of linear quantum oscillator with spin in vector optical tomography representation is considered and the evolution of initial entangled superposition of two lower Fock states and spin-up, spin-down states is studied in this representation.

arXiv:1412.7873Dec 26, 20140 citations

Quantum Tomography from the Evolution of a Single Expectation

Hjalmar Rall, Michael M. Wolf

arXiv:2501.10118Annales Henri PoincaréSep 10, 20250 citations

Partial symplectic quantum tomography schemes. Observables, evolution equations, and stationary states equations

Ya. A. Korennoy, V. I. Man'ko

Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are derived. Calculations were made by use of general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations. Taking the Gaussian functions as the distributions of the tomographic parameters the examples of joint probability representations were considered. Evolution equations and stationary states equations for partial symplectic conditional and joint probability distributions are obtained.Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are derived. Calculations were made by use of general formalism of quantizers and dequantizers determining the star product quantization scheme in these representations. Taking the Gaussian functions as the distributions of the tomographic parameters the examples of joint probability representations were considered. Evolution equations and stationary states equations for partial symplectic conditional and joint probability distributions are obtained.

arXiv:2406.06554May 30, 20240 citations

Calculations of the propagator within the tomographic-probability framework

Dmitry B. Lemeshevskiy, Vladimir I. Man’ko

Journal of Russian Laser ResearchSep 1, 20120 citations

Gauge transformation of quantum states in probability representation

Ya. A. Korennoy, Vladimir I. Man’ko

The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations having the Liouville equation in corresponding representations as the classical limit are found.The gauge invariance of the evolution equations of tomographic probability distribution functions of quantum particles in an electromagnetic field is illustrated. Explicit expressions for the transformations of ordinary tomograms of states under a gauge transformation of electromagnetic field potentials are obtained. Gauge-independent optical and symplectic tomographic quasi-distributions and tomographic probability distributions of states of quantum system are introduced, and their evolution equations having the Liouville equation in corresponding representations as the classical limit are found.

arXiv:1511.00364Nov 2, 20150 citations

\vec W({\mathbf q},{\mathbf p})

\vec Q({\mathbf q},{\mathbf p})

\vec P(\vecα)

are introduced. The evolution equations for proposed vector optical and symplectic tomograms and vector quasidistributions for arbitrary Hamiltonian are obtained. The quantum system of charged spin 1/2 particle in arbitrary electro-magnetic field is considered in proposed representations and evolution equations which are analogs of Pauli equation are obtained. The propagator of evolution equation in the case of homogeneous and stationary magnetic field in Landau gauge is found and the evolution of initial entangled superposition of lower Landau levels in the vector optical representation is considered. The system of linear quantum oscillator with spin in vector optical tomography representation is considered and the evolution of initial entangled superposition of two lower Fock states and spin-up, spin-down states is studied in this representation.