Measurable bounds for entanglement of formation

We study the entanglement of formation for arbitrary-dimensional bipartite mixed unknown states. Experimentally measurable lower and upper bounds for entanglement of formation are derived.

Figure 1

Upper and lower bounds of $E(\rho )$ (solid lines) for $m=3$, and $F_{11},F_{12}$, and $F_{21}$ (dashed line).

Figure 2

Upper and lower bounds of $E(\rho )$ (solid lines) for $m=4$, and $F_{11},F_{12},F_{21},F_{22},F_{13}$, and $F_{31}$(dashed line).

Figure 3

Upper and lower bounds of $E(\rho )$ with $x=0.1$.

Figure 4

Upper and lower bounds of $E(\rho )$ with $x=0.001$.