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Related Concept Videos

Discrete-time Fourier transform01:26

Discrete-time Fourier transform

The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
One of the notable...
Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Related Experiment Video

Updated: Jun 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Composable free-space continuous-variable quantum key distribution using discrete modulation.

Kevin Jaksch1,2,3, Thomas Dirmeier1,2, Yannick Weiser1,2

  • 1Max Planck Institute for the Science of Light, 91058 Erlangen, Germany.

Science Advances
|June 12, 2026
PubMed
Summary
This summary is machine-generated.

This study demonstrates a continuous-variable quantum key distribution system for atmospheric channels. It enables secure communication beyond fiber networks by calculating finite-size key rates for practical applications.

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Quasi-light Storage for Optical Data Packets
07:45

Quasi-light Storage for Optical Data Packets

Published on: February 6, 2014

Related Experiment Videos

Last Updated: Jun 14, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quasi-light Storage for Optical Data Packets
07:45

Quasi-light Storage for Optical Data Packets

Published on: February 6, 2014

Area of Science:

  • Quantum Information Science
  • Secure Communication Technologies
  • Optical Physics

Background:

  • Continuous-variable quantum key distribution (CV-QKD) offers secure communication, nearing classical coherent communication capabilities.
  • Discrete modulation in CV-QKD is practical for real-world devices, but experiments typically use asymptotic key rates.
  • Expanding CV-QKD beyond fiber optics is crucial for broader network integration.

Purpose of the Study:

  • To present a CV-QKD system optimized for atmospheric channels using discrete modulation.
  • To demonstrate the feasibility of CV-QKD for non-fiber based secure communication networks.
  • To calculate composable finite-size key rates for practical security assessments.

Main Methods:

  • Developed a CV-QKD system employing discrete modulation and polarization encoding.
  • Utilized the nonbirefringent property of the atmosphere for polarization encoding.
  • Implemented a recent security proof to calculate finite-size key rates against collective attacks.

Main Results:

  • Successfully demonstrated a CV-QKD system in a laboratory setting with a 3-dB loss channel.
  • Calculated composable finite-size key rates, moving beyond the asymptotic regime.
  • Integrated a quantum random number generator, error correction, and privacy amplification for key extraction.

Conclusions:

  • The developed CV-QKD system is suitable for atmospheric channels, expanding secure communication possibilities.
  • Finite-size key rate calculations provide a more realistic security measure for practical CV-QKD deployments.
  • Polarization encoding offers a viable strategy for CV-QKD in turbulent atmospheric environments.