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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
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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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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Confidence Polytopes in Quantum State Tomography.

Jinzhao Wang1, Volkher B Scholz1, Renato Renner1

  • 1Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland.

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|May 31, 2019
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Summary
This summary is machine-generated.

This study introduces a new method for quantum state tomography, providing reliable error bars for quantum state estimation. The approach generates efficient, polytope-shaped confidence regions for experimental use.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Statistical Inference

Background:

  • Quantum state tomography (QST) is crucial for characterizing quantum systems.
  • Accurate error quantification, beyond state estimation, is essential for reliable QST.
  • Existing methods often lack robust error estimation or are computationally intensive.

Purpose of the Study:

  • To develop a simple and reliable scheme for generating confidence regions in quantum state tomography.
  • To provide well-justified error bars for inferred quantum states.
  • To adapt classical statistical confidence intervals for quantum applications.

Main Methods:

  • Generalizing Clopper-Pearson confidence intervals from classical statistics to the quantum domain.
  • Developing a computational scheme to generate confidence regions with a polytope shape.
  • Testing the scheme's practical usability through experimental examples.

Main Results:

  • A novel, efficient scheme for computing confidence regions in QST.
  • The generated confidence regions are polytope-shaped, simplifying their representation.
  • Demonstrated practical applicability and reliability in experimental contexts.

Conclusions:

  • The proposed method offers a significant advancement in reliable quantum state tomography.
  • This scheme provides a practical tool for researchers to quantify uncertainty in quantum state estimation.
  • The generalization of classical statistical intervals opens new avenues for quantum data analysis.