Related papers: A one-to-two dimensional mapping using a partial f…
We propose a technique for performing quantum state tomography of photonic polarization-encoded multi-qubit states. Our method uses a single rotating wave plate, a polarizing beam splitter and two photon-counting detectors per photon mode.…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
We consider one-parameter families of quadratic-phase integral transforms which generalize the fractional Fourier transform. Under suitable regularity assumptions, we characterize the one-parameter groups formed by such transforms.…
This article addresses the problem of two- and higher dimensional pattern matching, i.e. the identification of instances of a template within a larger signal space, which is a form of registration. Unlike traditional correlation, we aim at…
The Quantum Fourier Transform (QFT) is a key component of many important quantum algorithms, most famously as being the essential ingredient in Shor's algorithm for factoring products of primes. Given its remarkable capability, one would…
The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with XX and ZZ couplings of neighboring qubits along and between the chains,…
Energy evaluation using fast Fourier transforms enables sampling billions of putative complex structures and hence revolutionized rigid protein-protein docking. However, in current methods efficient acceleration is achieved only in either…
The nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
The Fourier transform of two-point momentum-space Feynman integrals with massless propagators and two off-shell legs can be used to prove identities between their periods, exemplified by the glue-and-cut identity. We generalize this…
We have revisited Cooper's one pair problem of calculating the binding energy for two electrons, experiencing an attractive interaction near the Fermi surface, in case of quasi one dimensional lattice system. Though it is a generalized…
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing…
This letter is the first part of a three-part tutorial on orthogonal time frequency space (OTFS) modulation, which is a promising candidate waveform for future wireless networks. This letter introduces and compares two popular…
One of the major challenges of employing a dual-frequency phase-shifting algorithm for phase retrieval is its sensitivity to noise. Yun et. al [H Yun, B Li, S Zhang. 2017] proposed a dual-frequency method based on the Fourier transform…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.
We define a nonlinear Fourier transform which maps sequences of contractive $n \times n$ matrices to $SU(2n)$-valued functions on the circle $\mathbb{T}$. We characterize the image of finitely supported sequences and square-summable…
A two dimensional model of chiral bosons in non-commutative field space is considered in the framework of the Batalin-Fradkin-Tyutin (BFT) Hamiltonian embedding method converting the second-class constrained system into the first-class one.…
In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In ``Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang and A. Christlieb (2013), an efficient algorithm with…
A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces…