Quantifying Entanglement

Abstract

We present conditions every measure of entanglement has to satisfy and construct a whole class of 'good' entanglement measures. The generalization of our class of entanglement measures to more than two particles is straightforward. We present a measure which has a statistical operational basis that might enable experimental determination of the quantitative degree of entanglement.

Figures (1)

• Figure 1: The set of all density matrices, ${\cal T}$ is represented by the outer circle. Its subset, a set of disentangled states ${\cal D}$ is represented by the inner circle. A state $\sigma$ belongs to the entangled states, and $\rho^*$ is the disentangled state that minimizes the distance $D( \sigma || \rho)$, thus representing the amount of quantum correlations in $\sigma$. State $\rho^*_A \otimes \rho^*_B$ is obtained by tracing $\rho^*$ over $A$ and $B$. $D( \rho^* || \rho^*_A \otimes \rho^*_B)$ represent the classical part of correlations in the state $\sigma$.