Related papers: Quaternion representation and symplectic spin tomo…
We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with…
Quantum process tomography is used to fully characterize the evolution of the quantum vibrational state of atoms. Rubidium atoms are trapped in a shallow optical lattice supporting only two vibrational states, which we charcterize by…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
On one hand, the concept of Quantum Phase Space which is compatible with the uncertainty principle has been considered recently. It has also been shown that a natural symmetry that can be associated with this quantum phase space is the…
Spectroscopic measurements with low-temperature scanning tunneling microscopes have been used very successfully for studying not only individual atomic or molecular spins on surfaces but also complexly designed coupled systems. The symmetry…
We propose a tomographic reconstruction scheme for spin states. The experimental setup, which is a modification of the Stern-Gerlach scheme, can be easily performed with currently available technology. The method is generalized to…
Wigner's method of induced representations is applied to the N=1 super-Poincare group, and by using a state corresponding to the basic vector of the little group as a Clifford vacuum we show that the spin operator of a supersymmetric point…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
The full Schmidt decomposition of spatiotemporally entangled states generated from spontaneous parametric down-conversion (SPDC) has not been carried out until now due to the immense computational complexity arising from the large…
We propose and discuss `quantum spin lenses', where quantum states of delocalized spin excitations in an atomic medium are `focused' in space in a coherent quantum process down to (essentially) single atoms. These can be employed to create…
In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in…
We introduce the notion of regular symplectomorphism and graded regular symplectomorphism between singular phase spaces. Our main concern is to exhibit examples of unitary torus representations whose symplectic quotients cannot be graded…
Quantum state estimation is an important task of many quantum information protocols. We consider two families of unitary evolution operators, one with a one-parameter and the other with a two-parameter, which enable the estimation of a…
Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
There exist many attempts to define a Wigner function for qudits, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are artificial in their construction and do not allow…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
Muon spin rotation/relaxation/resonance (MuSR) technique for studying matter structures is considered by means of a recently introduced probability representation of quantum spin states. A relation between experimental MuSR histograms and…
This review covers latest developments in continuous-variable quantum-state tomography of optical fields and photons, placing a special accent on its practical aspects and applications in quantum information technology. Optical homodyne…
Here I present a new discrete model of quantum mechanics for relativistic 1-electron systems, in which particle movement is described by a directed space-time graph with attached 4-spinors, but without any continuous wave functions. These…