Quantum spectral analysis: frequency in time

Mario Mastriani

Mario Mastriani

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

Michael J. Biercuk

J. Nunn, Laura Jayne Wright, Christoph Söller +3 more

We introduce a novel time-frequency quantum key distribution (TFQKD) scheme based on photon pairs entangled in these two conjugate degrees of freedom. The scheme uses spectral detection and phase modulation to enable measurements in the temporal basis by means of time-to-frequency conversion. This allows large-alphabet encoding to be implemented with realistic components. A general security analysis for TFQKD with binned measurements reveals a close connection with finite-dimensional QKD protocols and enables analysis of the effects of dark counts on the secure key size.

Vincent Crozatier, V. Lavielle, Fabien Bretenaker +2 more

We demonstrate implementation of the chirp transform algorithm with photon echoes in an Er/sup 3+/:YSO crystal at 1536 nm for application to spectral analysis of RF signals. The principle and features of the technique are presented using a simple picture in the time-frequency plane. Experimental results with low-bandwidth RF signals demonstrate 40-kHz spectral resolution and a time-bandwidth product of 500. Extension to broad-band RF signals is discussed.

V. V. Ul'yanov, V. D. Babenko