Related papers: Star product and ordered moments of photon creatio…
In this paper, we formulate the phase space description of qubit systems using coadjoint orbits of $SU(2)$ and the Stratonovich-Weyl correspondence, yielding a deformation quantization on the sphere. The resulting star product reproduces…
We consider atoms in two different periodic potentials induced by different lasers, one of which is coupled to a mechanical membrane via radiation pressure force. The atoms are intrinsically two-level systems that can absorb or emit…
A star-product formalism describing deformations of the standard quantum mechanical harmonic oscillator is introduced. A number of existing generalized oscillators occur as particular choises of star-products between the elements of the…
Columns of d^2 x N matrices are shown to create different sets of N operators acting on $d$-dimensional Hilbert space. This construction corresponds to a formalism of the star-product of operator symbols. The known bases are shown to be…
We study continuous phase spaces of single spins and develop a complete description of their time evolution. The time evolution is completely specified by so-called star products. We explicitly determine these star products for general spin…
The quantization of the second-class constraint systems is discussed within the projection operator method(POM) of constraint systems. Through the nonlocal representation of the constraint hyper-operators, new star-products are defined.…
A duality property for star products is exhibited. In view of it, known star-product schemes, like the Weyl-Wigner-Moyal formalism, the Husimi and the Glauber-Sudarshan maps are revisited and their dual partners elucidated. The tomographic…
In this paper we construct non-equivalent star products on CP^n by phase space reduction. It turns out that the non-equivalent star products occur very natural in the context of phase space reduction by deforming the momentum map of the…
Two measurable characteristics of microwave one-mode photon states are discussed: a rotated quadrature distribution (tomogram) and normally/antinormally ordered moments of photon creation and annihilation operators. Extraction of these…
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…
The quantizer-dequantizer formalism is developed for mean value and probability representation of qubits and qutrits. We derive the star-product kernels providing the possibility to derive explicit expressions of the associative product of…
The geometric picture of the star-product based on its Fourier representation kernel is utilized in the evaluation of chains of star-products and the intuitive appreciation of their associativity and symmetries. Such constructions appear…
We show how one can deterministically generate photonic matrix product states with high bond and physical dimensions with an atomic array if one has access to a Rydberg-blockade mechanism. We develop both a quantum gate and an optimal…
We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…
Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…
We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus…
We present a time-dependent density-matrix renormalization group investigation of the quantum distillation process within the Fermi--Hubbard model on a quasi-1D ladder geometry. The term distillation refers to the dynamical, spatial…
We study quantization via star products. We investigate a quantization scheme in which a quantum theory is described entirely in terms of the function space without reference to a Hilbert space, unlike the formulation employing the Wigner…
A new integral representation is obtained for the star product corresponding to the $s$-ordering of the creation and annihilation operators. This parametric ordering convention introduced by Cahill and Glauber enables one to vary the type…
Time crystals are nonequilibrium phases of matter characterized by the emergence of temporal ordering, in which an interacting many-body system develops robust structure in its time evolution that is not trivially dictated by the external…