Example of Completely positive map from M_n to M_m

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SUMMARY

A completely positive map from M_m to M_n is a linear map that preserves positivity when applied to positive semidefinite matrices. A concrete example is the map defined by the matrix A, where A is a positive semidefinite matrix in M_m. This map can be expressed as φ(X) = A * X * A^*, where X is any matrix in M_m. Understanding completely positive maps is essential for applications in quantum mechanics and operator algebras.

PREREQUISITES
  • Understanding of matrix theory and linear algebra
  • Familiarity with positive semidefinite matrices
  • Knowledge of operator algebras
  • Basic concepts of quantum mechanics
NEXT STEPS
  • Research the properties of completely positive maps in operator theory
  • Study the relationship between positive-definite and completely positive maps
  • Explore applications of completely positive maps in quantum information theory
  • Learn about the Choi-Kraus representation of completely positive maps
USEFUL FOR

Mathematicians, physicists, and researchers in quantum information theory who are looking to deepen their understanding of completely positive maps and their applications in various fields.

Genericcoder
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Can you guys give me a concrete example of a completely positive map from M_m → M_n?
 
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I'm sorry you are not generating any responses at the moment. Is there any additional information you can share with us? Any new findings?
 
Genericcoder said:
Can you guys give me a concrete example of a completely positive map from M_m → M_n?

Could you please define it for us? I'm used to positive-definite maps, but not completely-positive ones.
 

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