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Related Concept Videos

Correlation of Experimental Data01:23

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...
Correlations02:20

Correlations

Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
Correlation01:09

Correlation

In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
Correlation and Regression00:53

Correlation and Regression

In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a negative...
Correlation and Causation01:27

Correlation and Causation

Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
Correlation versus Causation
If the dependent variable increases or decreases when the independent variable increases, there is a positive or negative...
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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Operational approach to open dynamics and quantifying initial correlations.

Kavan Modi1

  • 1Department of Physics, University of Oxford Clarendon Laboratory, Oxford OX1 3PU, UK. kavan@quantumlah.org

Scientific Reports
|August 17, 2012
PubMed
Summary
This summary is machine-generated.

This study presents a new quantum process tomography method to describe quantum system dynamics. It accurately captures system evolution even with initial environmental correlations, providing quantitative expressions for these correlations.

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Area of Science:

  • Quantum physics
  • Quantum information science
  • Statistical mechanics

Background:

  • Describing quantum system dynamics interacting with environments is challenging due to environmental state dependence and correlations.
  • Standard quantum process tomography assumes initial independence between system and environment, limiting its applicability.
  • Many real-world quantum systems exhibit initial correlations with their environment.

Purpose of the Study:

  • To develop a quantum process tomography method applicable to systems with initial environmental correlations.
  • To provide a complete description of quantum system dynamics under general conditions.
  • To quantify initial correlations between quantum systems and their environments.

Main Methods:

  • A novel prescription for quantum process tomography is proposed.
  • The method extends the capabilities of quantum process tomography to scenarios with pre-existing system-environment correlations.
  • Mathematical framework is developed to derive dynamics and initial correlations.

Main Results:

  • The developed quantum process tomography successfully describes quantum system dynamics even with initial correlations.
  • The method provides quantitative expressions for these initial system-environment correlations.
  • This overcomes a key limitation of previous quantum process tomography techniques.

Conclusions:

  • The proposed quantum process tomography offers a more general approach to characterizing quantum dynamics.
  • It enables the study of quantum systems interacting with correlated environments.
  • The ability to quantify initial correlations opens new avenues for understanding and controlling quantum systems.