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Related Concept Videos

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 Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
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¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
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Related Experiment Video

Updated: Jun 8, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Four-qubit entanglement classification from string theory.

L Borsten1, D Dahanayake, M J Duff

  • 1Theoretical Physics, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom. leron.borsten@imperial.ac.uk

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Researchers used the black-hole-qubit correspondence to classify four-qubit entanglement. String theory reductions revealed 31 entanglement families, simplifying to nine distinct types.

Related Experiment Videos

Last Updated: Jun 8, 2026

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Area of Science:

  • Theoretical Physics
  • Quantum Information Science
  • String Theory

Background:

  • The black-hole-qubit correspondence provides a novel framework for studying quantum entanglement.
  • String theory compactifications offer a rich landscape for exploring complex quantum systems.

Purpose of the Study:

  • To classify all possible four-qubit entanglement states using the black-hole-qubit correspondence.
  • To investigate the relationship between U-duality orbits in string theory and entanglement structures.

Main Methods:

  • Applying the black-hole-qubit correspondence to analyze four-qubit systems.
  • Performing timelike reductions of string theory from D=4 to D=3 dimensions.
  • Classifying entanglement families based on U-duality orbits.

Main Results:

  • Derived a complete classification of four-qubit entanglement.
  • Identified 31 distinct entanglement families arising from U-duality orbits.
  • Reduced the number of unique entanglement families to nine, considering qubit permutations.

Conclusions:

  • The black-hole-qubit correspondence is a powerful tool for understanding multipartite entanglement.
  • String theory compactifications naturally encode complex entanglement structures.
  • A concise classification of four-qubit entanglement has been established.