Related papers: Quantum Optical Version of Classical Optical Trans…

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

Corresponding to Fresnel transform there exists a unitary operator in quantum optics theory, which could be named Fresnel operator (FO). We show that the multiplication rule of FO naturally leads to the quantum optical ABCD law. The…

Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…

The paper scrutinizes both the similarities and the differences between the classical optics and quantum mechanical theories in phase space, especially between the Wigner distribution functions defined in the respective phase spaces.…

Circular and hyperbolic fractional-order Fourier transformations are actually Weyl pseudo-differential operators. Their associated kernels and symbols are written explicitly. Products of fractional-order Fourier transformations are obtained…

All-quantum signal processing techniques are at the core of the successful advancement of most information-based quantum technologies. This paper develops coherent and comprehensive methodologies and mathematical models to describe Fourier…

The symplectic wavelet transformation [Opt. Lett. 31 (2006) 3432], which is related to quantum optical Fresnel transform, is developed to the symplectic-dilation mixed wavelet transform (SDWT). The SDWT involves both a real-variable…

By utilizing quantum optics techniques, we examine the characteristics of a quantum gravitational wave (GW) signature at interferometers. In particular, we study the problem by analyzing the equations of motion of a GW interacting with an…

We introduce the quantum fractional Hadamard transform with continuous variables. It is found that the corresponding quantum fractional Hadamard operator can be decomposed into a single-mode fractional operator and two single-mode squeezing…

Continuous-variables (CV) quantum optics is a natural formalism for neural networks (NNs) due to its ability to reproduce the information processing of such trainable interconnected systems. In quantum optics, Gaussian operators induce…

Modern quantum optics primarily operates in the quasistationary regime, isolated from the intrinsic timescales of ultrafast optical fields. Pushing these boundaries into the femtosecond and attosecond domains is a critical frontier. Here,…

We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This…

We study the classical optics effects known as Goos-H\"anchen (GH) and Imbert-Fedorov (IF) shifts, occurring when reflecting a bounded light beam from a planar surface, by using a quantum-mechanical formalism. This new approach allows us to…

A new model of quantum computing has recently been proposed which, in analogy with a classical lambda-calculus, exploits quantum processes which operate on other quantum processes. One such quantum meta-operator takes N unitary…

The manipulation of distinct degrees of freedom of photons plays a critical role in both classical and quantum information processing. While the principles of wave optics provide elegant and scalable control over classical light in spatial…

Using the notions of frame transform and of square integrable projective representation of a locally compact group $G$, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier…

The theory of quantum propagator and time--dependent integrals of motion in quantum optics is reviewed as well as the properties of Wigner function, Q--function, and coherent state representation. Propagators and wave functions of a free…

We demonstrate that a tensor product structure and optical analogy of quantum entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical analogy, we discuss…

Corresponding to optical Fresnel transformation characteristic of ray transfer matrix elements (A;B;C;D); AD-BC = 1, there exists Fresnel operator F(A;B;C;D) in quantum optics, we show that under the Fresnel transformation the pure position…

A convenient way to represent quantum optical states is through the quadrature basis of single-modes of the field. This framework provides intuitive definitions for quasi-classical states, their phase-space representations, and enables the…