Related papers: Enhanced quantization on the circle
We discuss the relation between quantum curves (defined as solutions of equation $[P,Q]=\hbar$, where $P,Q$ are ordinary differential operators) and classical curves. We illustrate this relation for the case of quantum curve that…
A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
A certain non-linear non-local substitution is shown to transform the action of the self-interacting quantum field to the free one. The functional integrals in both theories are equal to each other. However, the integrations are performed…
We show that quantum operations on multi-particle systems have a non-local content; this mirrors the non-local content of quantum states. We introduce a general framework for discussing the non-local content of quantum operations, and give…
Motivated by various systems in which quantum effects occur in classical backgrounds, we consider the dynamics of a classical particle as described by a coherent state that is coupled to a quantum bath via bi-quadratic interactions. We…
We investigate the behaviour of a particle moving on the quotient manifold $M=C^2/Z_$ which is derived from the EH metric as the two centers approach each other. In the classical region of the configuration space we specify the physically…
We study the quantization of a model proposed by Newton to explain centripetal force namely, that of a particle moving on a regular polygon. The exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a particle moving…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
Canonical quantization of an action containing curvature squared term requires introduction of an auxiliary variable. Boulware etal[1] prescribed a technique to choose such a variable, by taking derivative of an action with respect to the…
We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum…
The generalized Einstein action is treated quantum mechanically by using a quadratic lagrangian form. The canonical quantization of this action is obtained by using the auxiliary variable to define the generalized momentum. Physical…
This note shows how quantum entanglement may be simulated in classical computing. The simulated entanglement protocol is implemented using oblivious transfer in the simplest case and other many-to-one mappings in more general cases. For the…
A classical circularly polarized electromagnetic wave carries angular momentum, and represents the classical limit of a photon, which carries quantized spin. It is shown that a very similar picture of a circularly polarized coherent wave…
The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in…
The quantum contributions to the gravitational action are relatively easy to calculate in the higher derivative sector of the theory. However, the applications to the post-inflationary cosmology and astrophysics require the corrections to…
We study the problem of the practical realization of an abstract quantum circuit when executed on quantum hardware. By practical, we mean adapting the circuit to particulars of the physical environment which restricts/complicates the…
Using extended Schwinger's quantization approach quantum mechanics on a Riemannian manifold $M$ with a given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally…
Quantum entanglement plays an important role in quantum computation and communication. It is necessary for many protocols and computations, but causes unexpected disturbance of computational states. Hence, static analysis of quantum…