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Related Concept Videos

Quantum Numbers02:43

Quantum Numbers

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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.
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Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

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Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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Hybridization of Atomic Orbitals II03:35

Hybridization of Atomic Orbitals II

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sp3d and sp3d 2 Hybridization
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Maxam-Gilbert Sequencing01:05

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In the same year as the discovery of the Sanger sequencing method, another group of scientists, Allan Maxam and Walter Gilbert, demonstrated their chemical-cleavage method for DNA sequencing. The Maxam-Gilbert method relies on using different chemicals that can cleave the DNA sequence at specific sites, the separation of resulting DNA fragments of variable size using electrophoresis, and deciphering the DNA sequence from the resulting gel bands.
Challenges of the Maxam-Gilbert Method
The...
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Hybridization of Atomic Orbitals I03:24

Hybridization of Atomic Orbitals I

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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)01:22

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1.1K
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...
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Updated: Sep 20, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
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Entanglement-assisted concatenated quantum codes.

Jihao Fan1, Jun Li2, Yongbin Zhou1

  • 1School of Cyber Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China.

Proceedings of the National Academy of Sciences of the United States of America
|June 10, 2022
PubMed
Summary
This summary is machine-generated.

Entanglement-assisted concatenated quantum codes (EACQCs) offer superior error correction compared to standard codes. These advanced quantum error-correction codes (QECCs) achieve better performance even with noisy entangled qubits.

Keywords:
concatenated quantum codeentanglement fidelityentanglement-assisted quantum error-correction codeerror-correction codequantum Hamming bound

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Quantum Communication

Background:

  • Standard concatenated quantum codes (CQCs) have limitations in achieving optimal error correction thresholds.
  • Entanglement-assisted quantum error-correction codes (EAQECCs) offer a framework for enhanced quantum error correction.
  • The performance of quantum error correction is often limited by the noise in quantum bits (qubits) and entangled pairs (ebits).

Purpose of the Study:

  • To propose and analyze entanglement-assisted concatenated quantum codes (EACQCs) as an advancement over standard CQCs.
  • To demonstrate the theoretical and practical advantages of EACQCs in quantum error correction and communication.
  • To investigate the performance of EACQCs under noisy conditions, particularly with imperfect entangled pairs.

Main Methods:

  • Construction of EACQCs by concatenating two quantum codes.
  • Theoretical analysis to prove EACQCs can surpass the nondegenerate Hamming bound for EAQECCs.
  • Derivation of error-probability thresholds for EACQCs and comparison with CQCs under various noise models.

Main Results:

  • EACQCs demonstrate the ability to exceed the nondegenerate Hamming bound, outperforming standard CQCs.
  • New families of EACQCs are constructed with parameters superior to existing QECCs and EAQECCs.
  • EACQCs maintain entanglement fidelity and enable quantum communication even with noisy ebits, showing a high error threshold of 47% when ebit error probability is 1%.

Conclusions:

  • EACQCs represent a significant improvement in quantum error correction, offering enhanced performance and robustness.
  • The proposed EACQCs require minimal entangled pairs (ebits) for implementation, making them practical.
  • EACQCs provide a viable approach for reliable quantum communication over noisy channels, outperforming traditional methods.