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Separability Criteria Based on the Weyl Operators.

Xiaofen Huang1,2, Tinggui Zhang1,2, Ming-Jing Zhao3

  • 1School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, China.

Entropy (Basel, Switzerland)
|August 26, 2022
PubMed
Summary
This summary is machine-generated.

We introduce a new quantum state decomposition using the Weyl basis to analyze entanglement. This method effectively detects entanglement in various quantum states and aids quantum teleportation.

Keywords:
Bloch representationWeyl operatorscorrelation matrixquantum teleportationseparability

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Area of Science:

  • Quantum Information Science
  • Quantum State Characterization
  • Entanglement Theory

Background:

  • Entanglement is a crucial resource in quantum information processing.
  • Understanding and quantifying entanglement is essential for developing quantum technologies.
  • Existing methods for analyzing quantum states have limitations in detecting certain types of entanglement.

Purpose of the Study:

  • To propose a novel Bloch decomposition of quantum states using the Weyl basis.
  • To develop an alternative characterization of quantum state separability.
  • To establish an effective criterion for detecting entanglement in various quantum states and for quantum teleportation.

Main Methods:

  • Utilized the Weyl basis for a new Bloch decomposition of quantum states.
  • Investigated the separability problem of quantum states using this decomposition.
  • Derived a separability criterion based on the correlation matrix.
  • Constructed a detecting operator for quantum teleportation using Weyl operators.

Main Results:

  • The proposed Weyl decomposition provides an alternative characterization of quantum state separability.
  • The derived criterion is effective in detecting entanglement for isotropic states, Bell-diagonal states, and some positive partial transpose (PPT) entangled states.
  • A detecting operator for quantum teleportation was successfully constructed.

Conclusions:

  • The Weyl decomposition offers a new perspective on analyzing quantum states and their entanglement.
  • The developed separability criterion enhances the ability to identify entangled states.
  • This work contributes to the advancement of quantum information processing and quantum communication protocols like teleportation.