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Related Concept Videos

Frequency-dependent Selection01:21

Frequency-dependent Selection

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.Positive Frequency-Dependent SelectionIn positive...
Quantum Numbers02:43

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
The Quantum-Mechanical Model of an Atom02:45

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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

Woodward–Hoffmann Selection Rules and Microscopic Reversibility

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...
The Role of Ion Channels in Neuronal Computation01:19

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A postsynaptic neuron usually receives numerous impulses from several other presynaptic neurons. The axon hillock of the postsynaptic neuron integrates all these signals and determines the likelihood of firing an action potential.
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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Related Experiment Video

Updated: Jun 25, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Postselection technique for quantum channels with applications to quantum cryptography.

Matthias Christandl1, Robert König, Renato Renner

  • 1Faculty of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany.

Physical Review Letters
|March 5, 2009
PubMed
Summary
This summary is machine-generated.

We present a new method to study quantum channels on multi-part systems. It simplifies analysis by showing that only specific de Finetti-type states need to be considered for arbitrary inputs.

Related Experiment Videos

Last Updated: Jun 25, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Information Theory
  • Quantum Cryptography

Background:

  • Studying quantum channels on n-partite systems is complex.
  • Permutation-invariant properties simplify analysis.
  • De Finetti theorems relate multi-partite states to single-system states.

Purpose of the Study:

  • To develop a general method for analyzing properties of permutation-invariant quantum channels.
  • To simplify proofs for information-theoretic problems in quantum systems.
  • To provide tighter security bounds for quantum cryptography protocols.

Main Methods:

  • Developing a general method for studying permutation-invariant quantum channels.
  • Utilizing de Finetti-type states (n identical and independent copies of a single subsystem state) as a sufficient input for analysis.
  • Applying the technique to quantum cryptography, specifically discrete-variable quantum key distribution.

Main Results:

  • A general method for studying permutation-invariant quantum channels on n-partite systems is proposed.
  • It is sufficient to consider de Finetti-type states to prove properties for arbitrary inputs.
  • Security of discrete-variable quantum key distribution against collective attacks is shown to imply security against general attacks.

Conclusions:

  • The proposed method simplifies the analysis of quantum channels.
  • The technique offers a more straightforward path to proving security in quantum cryptography.
  • The derived security bounds are improved compared to previous methods.