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 $\rho _{AB}=|\Psi \rangle \langle \Psi |$, it is given by:

${\mathcal {E}}(\rho _{AB})={\mathcal {S}}(\rho _{A})={\mathcal {S}}(\rho _{B})$

where ${\mathcal {S}}$ is the von Neumann entropy, $\rho _{A}=\mathrm {Tr} _{B}(\rho _{AB})$ and $\rho _{B}=\mathrm {Tr} _{A}(\rho _{AB})$.

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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