Convergent matrix

The entropy of entanglement is an entanglement measure for a bipartite pure states. It is defined as the von Neumann entropy of one of the reduced states. That is, for a pure state ${\rho }_{AB}=|\mathrm{\Psi }⟩⟨\mathrm{\Psi }|$, it is given by:

$\mathcal{ℰ}({\rho }_{AB})=\mathcal{𝒮}({\rho }_A)=\mathcal{𝒮}({\rho }_B)$

where $\mathcal{𝒮}$ is the von Neumann entropy, ${\rho }_A={\mathrm{T}\mathrm{r}}_B({\rho }_{AB})$ and ${\rho }_B={\mathrm{T}\mathrm{r}}_A({\rho }_{AB})$.

Many entanglement measures reduce to the entropy of entanglement when evaluated on pure states. Among those are:

• Distillable entanglement
• Entanglement cost
• Entanglement of formation
• Relative entropy of entanglement
• Squashed entanglement

Some entanglement measures that do not reduce to the entropy of entanglement are:

• Negativity
• Logarithmic negativity
• Robustness of entanglement

References/sources

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