Next Article in Journal
Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations
Next Article in Special Issue
The Spinor-Tensor Gravity of the Classical Dirac Field
Previous Article in Journal
Asymmetric Membranes: A Potential Scaffold for Wound Healing Applications
Previous Article in Special Issue
Representing Measurement as a Thermodynamic Symmetry Breaking
 
 
Article

SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics

1
Institute for Solid State Physics and Optics, Wigner Research Center for Physics, P.O. Box 49, H-1525 Budapest, Hungary
2
Institute of Physics, University of Pécs, Ifjúság útja 6, H-7624 Pécs, Hungary
3
Lebedev Physical Institute, Leninskii Prospect 53, Moscow 119991, Russia
4
Moscow Institute of Physics and Technology, State University, Institutskii per. 9, Dolgoprudnyi, Moscow Region 141700, Russia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(7), 1099; https://doi.org/10.3390/sym12071099
Received: 18 April 2020 / Revised: 8 May 2020 / Accepted: 10 May 2020 / Published: 2 July 2020
(This article belongs to the Special Issue Symmetry in Quantum Systems)
In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ± 1 / 2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties. View Full-Text
Keywords: quantum tomography; probability representation; quantizer–dequantizer; qubit quantum tomography; probability representation; quantizer–dequantizer; qubit
MDPI and ACS Style

Adam, P.; Andreev, V.A.; Man’ko, M.A.; Man’ko, V.I.; Mechler, M. SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics. Symmetry 2020, 12, 1099. https://doi.org/10.3390/sym12071099

AMA Style

Adam P, Andreev VA, Man’ko MA, Man’ko VI, Mechler M. SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics. Symmetry. 2020; 12(7):1099. https://doi.org/10.3390/sym12071099

Chicago/Turabian Style

Adam, Peter, Vladimir A. Andreev, Margarita A. Man’ko, Vladimir I. Man’ko, and Matyas Mechler. 2020. "SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics" Symmetry 12, no. 7: 1099. https://doi.org/10.3390/sym12071099

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop