The quantum state vector in phase space and Gabor's windowed Fourier transform

Real Clifford Windowed Fourier Transform

We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation, reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to ...

On the inverse windowed Fourier transform

The inversion problem concerning the windowed Fourier transform is considered. It is shown that, out of the infinite solutions that the problem admits, the windowed Fourier transform is the “optimal” solution according to a maximum-entropy selection criterion.

Fourier-transform quantum state tomography

We propose a technique for performing quantum state tomography of photonic polarization-encoded multiqubit states. Our method uses a single rotating wave plate, a polarizing beam splitter, and two photon-counting detectors per photon mode. As the wave plate rotates, the photon counters measure a pseudocontinuous signal which is then Fourier transformed. The density matrix of the state is recons...

Oversampled Windowed Fourier Transform and Filter Banks

Quantum Fourier transform of the Prime state

Quantum Computation is a growing and important field in applied physics research, so further theoretical foundations are continuously requested. In this regard, some mathematical algorithms have already been proposed. For instance, creating a quantum state representing the superposition of all prime number less than a value N has been shown to be efficient, and also applying the Quantum Fourier...