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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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A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
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When analyzing beams under unsymmetrical loads, such as a train moving on a bridge, it is crucial to accurately determine the points of maximum stress and deflection. The process involves identifying the maximum deflection of the beam, which may not always occur at its midpoint due to the uneven distribution of the load.
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The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. Like the histogram, a relative frequency histogram also has the same shape with a horizontal scale (the x-axis), but the vertical scale (the y-axis) is marked with relative frequencies (percentages of the whole) instead of actual frequencies. A relative frequency histogram is a graphical representation of a frequency distribution where the...
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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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Updated: Jan 26, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quadrature histograms in maximum-likelihood quantum state tomography.

J L E Silva1, S Glancy2, H M Vasconcelos1,2

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Summary

Discretizing continuous variable measurements in quantum state tomography reduces computation time. This method maintains high fidelity for estimating quantum states of light, essential for quantum information science.

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Area of Science:

  • Quantum Information Science
  • Quantum Optics
  • Quantum Measurement

Background:

  • Quantum state tomography is crucial for characterizing quantum systems.
  • Continuous variable quantum states of light are often studied using homodyne detection.
  • Discretizing measurements is a common technique to reduce computational cost in tomography.

Purpose of the Study:

  • To investigate strategies for discretizing continuous variable measurements in quantum state tomography.
  • To determine the impact of histogram bin width selection on state estimation fidelity.
  • To optimize computational efficiency in quantum state tomography without sacrificing accuracy.

Main Methods:

  • Analyzing different strategies for setting histogram bin widths in quadrature-phase homodyne detection.
  • Integrating measurement operators over chosen bin widths.
  • Comparing the fidelity of estimated quantum states using discretized versus continuous measurements.

Main Results:

  • Discretization of continuous variable measurements can be performed without significant loss in state estimation fidelity.
  • Specific strategies for determining histogram bin widths were evaluated.
  • Integrating measurement operators over bin widths significantly reduces computation time.

Conclusions:

  • Discretizing continuous variable measurements is a viable approach for quantum state tomography.
  • Optimized bin width selection and operator integration offer computational advantages.
  • This method enhances the practicality of quantum state tomography for continuous variable systems.