Entanglement

Quantum Mechanics · Part 9

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Table of Contents

  1. 1.Product States vs. Entangled States
  2. 2.Bell States: Maximally Entangled Pairs
  3. 3.Schmidt Decomposition
  4. 4.Density Matrix of a Subsystem
  5. 5.Entanglement Entropy
  6. 6.Purity and the Entanglement Connection
  7. 7.Detecting Entanglement: Witnesses and the PPT Criterion
  8. 8.Proof Sketch
  9. 9.Schmidt Number as Entanglement Measure
  10. 10.Example: Bell State Entanglement

Key Equations

$$|\psi\rangle_{AB} = |\phi\rangle_A \otimes |\chi\rangle_B$$
$$|\Psi^+\rangle = \frac{1}{\sqrt{2}}\left(|01\rangle + |10\rangle\right), \qquad |\Psi^-\rangle = \frac{1}{\sqrt{2}}\left(|01\rangle - |10\rangle\right)$$
$$\boxed{S(\hat{\rho}_A) = -\text{Tr}\!\left(\hat{\rho}_A \ln\hat{\rho}_A\right) = -\sum_{i=1}^{r} \lambda_i \ln\lambda_i}$$
$$\gamma(\hat{\rho}_A) = \text{Tr}\!\left(\hat{\rho}_A^2\right) = \sum_i \lambda_i^2$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Quantum Mechanics course on CoursesHub.World. Master quantum mechanics from mathematical foundations to advanced topics. Covers Hilbert spaces, wave functions, angular momentum, perturbation theory, scattering, and path integrals with 450+ pages ...

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