  We generalize previously proposed conditions each measure of entanglement has
to satisfy. We present a class of entanglement measures that satisfy these
conditions and show that the Quantum Relative Entropy and Bures Metric generate
two measures of this class. We calculate the measures of entanglement for a
number of mixed two spin 1/2 systems using the Quantum Relative Entropy, and
provide an efficient numerical method to obtain the measures of entanglement in
this case. In addition, we prove a number of properties of our entanglement
measure which have important physical implications. We briefly explain the
statistical basis of our measure of entanglement in the case of the Quantum
Relative Entropy. We then argue that our entanglement measure determines an
upper bound to the number of singlets that can be obtained by any purification
procedure and that distillable entanglement is in general smaller than the
entanglement of creation.

Quantum Physics