Related papers: Three paths toward the quantum angle operator
The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…
Quantum nonlinear operations for harmonic oscillator systems play a key role in the development of analog quantum simulators and computers. Since a variety of strong highly nonlinear operations are unavailable in the existing physical…
In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving…
Bessel beams are studied within the general framework of quantum optics. The two modes of the electromagnetic field are quantized and the basic dynamical operators are identified. The algebra of these operators is analyzed in detail; it is…
In this contribution a path integral approach for the quantum motion on three-dimensional spaces according to Koenigs, for short``Koenigs-Spaces'', is discussed. Their construction is simple: One takes a Hamiltonian from three-dimensional…
We employ an algebraic procedure based on quantum mechanics to propose a `quantum number theory' (QNT) as a possible extension of the `classical number theory'. We built our QNT by defining pure quantum number operators ($q$-numbers) of a…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
We construct quantum gates entanglers for different classes of multipartite states. In particular we construct entangler operators for W and GHZ classes of multipartite states based on the construction of the concurrence classes. We also in…
The recent developments of electron quantum optics in quantum Hall edge channels have given us new ways to probe the behavior of electrons in quantum conductors. It has brought new quantities called electronic coherences under the…
Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…
We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
The domain of application of quantization methods is traditionally restricted to smooth classical observables. We show that the coherent states or "anti-Wick" quantization enables us to construct fairly reasonable quantum versions of…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
The problem of estimating a generic phase-shift experienced by a quantum state is addressed for a generally degenerate phase shift operator. The optimal positive operator-valued measure is derived along with the optimal input state. Two…
A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in…