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Related Concept Videos

Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Operational quantification of continuous-variable correlations.

Carles Rodó1, Gerardo Adesso, Anna Sanpera

  • 1Grup de Física Teòrica, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.

Physical Review Letters
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

We developed a method to quantify quantum correlations using extracted bits from measurements. This technique offers a practical way to measure non-Gaussian entanglement in experiments without full state tomography.

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Area of Science:

  • Quantum information science
  • Quantum optics
  • Quantum entanglement

Background:

  • Quantifying quantum correlations is crucial for understanding quantum information processing.
  • Entanglement is a key quantum resource, but its quantification can be experimentally challenging.
  • Distinguishing quantum from classical correlations requires robust measures.

Purpose of the Study:

  • To introduce and quantify
  • bit quadrature correlations
  • as a measure of quantum correlations.
  • To establish a connection between bit quadrature correlations and entanglement.
  • To provide an experimentally feasible method for measuring non-Gaussian entanglement.

Main Methods:

  • Quantifying correlations via the maximal number of correlated bits extracted from local quadrature measurements.
  • Analyzing the behavior of bit quadrature correlations on Gaussian and non-Gaussian states.
  • Comparing bit quadrature correlations with entanglement monotones and negativity.

Main Results:

  • Bit quadrature correlations majorize entanglement for Gaussian states, acting as an entanglement monotone for pure states.
  • For non-Gaussian states, bit correlations monotonically increase with negativity.
  • Demonstrated that bit quadrature correlations are a monotonic function of negativity for various non-Gaussian states.

Conclusions:

  • Bit quadrature correlations offer a feasible and operational method for quantifying non-Gaussian entanglement.
  • This approach enables experimental measurement using direct homodyne detection, bypassing the need for complete state tomography.
  • The findings provide a practical tool for advancing quantum information technologies.