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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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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.
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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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To achieve precise distance measurements, especially in surveying and construction, certain corrections must be applied to account for potential sources of error like the standardization errors, temperature variations, and slope adjustments.Standardization error emerges when measurement equipment undergoes changes, such as wear, repairs, or weather impacts. To address this, surveyors compare the equipment’s readings to a standard. This process identifies any deviation that might lead to...
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Gradient Echo Quantum Memory in Warm Atomic Vapor
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Achieving the Heisenberg limit in quantum metrology using quantum error correction.

Sisi Zhou1,2, Mengzhen Zhang3,4, John Preskill5

  • 1Departments of Applied Physics and Physics, Yale University, New Haven, CT, 06511, USA. sisi.zhou@yale.edu.

Nature Communications
|January 10, 2018
PubMed
Summary

Quantum error correction can achieve the Heisenberg limit for measurement precision, even with noisy quantum systems. This method protects quantum probes from noise, enabling enhanced precision in scientific and technological applications.

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Area of Science:

  • Quantum physics
  • Metrology
  • Information science

Background:

  • Quantum metrology offers fundamental limits on measurement precision (Heisenberg limit).
  • Noise in quantum systems prevents achieving the Heisenberg limit in general.
  • Quantum error correction is a method to protect quantum systems from noise.

Purpose of the Study:

  • Investigate enhancing measurement precision using quantum error correction.
  • Determine conditions for achieving the Heisenberg limit in noisy quantum probes.
  • Develop methods for optimal quantum error-correcting codes for metrology.

Main Methods:

  • Studied quantum probes subject to Markovian noise.
  • Assumed availability of noiseless ancilla systems and fast quantum processing.
  • Utilized semidefinite programming to find optimal quantum error-correcting codes.

Main Results:

  • Found a necessary and sufficient condition for achieving the Heisenberg limit with noisy quantum probes.
  • Demonstrated that quantum error correction can suppress noise without obscuring the signal.
  • Showed that optimal codes, maximizing precision, can be found via semidefinite programming.

Conclusions:

  • Quantum error correction is a viable strategy to overcome noise limitations in quantum metrology.
  • Achieving the Heisenberg limit is possible under specific conditions using quantum error correction.
  • The developed methods provide a pathway to enhanced precision in quantum measurements.